Ukraine urged civilians to leave the eastern Donetsk, Luhansk and parts of the Kharkiv regions as it braced for a major new Russian offensive following Moscow’s withdrawal from the north of the country.

“You need to evacuate now, while this possibility still exists,” Ukraine’s deputy prime minister and minister for occupied territories, Iryna Vereshchuk, said on Ukrainian TV on Wednesday. “Later, people will be under fire and under threat of death. We won’t be able to help because it will be practically impossible to cease fire.”

The sense of urgency by the Ukrainian government for civilians to flee comes days after reports emerged of executions, rape and other human rights abuses of civilians by departing Russian forces as they retreated from the suburbs of Kyiv. Russia has denied the reports and said they were staged by Ukrainian troops.

Following heavy losses, Russia pulled its troops from the vicinity of Kyiv and from the northern Chernihiv and Sumy regions last week, in a strategy shift that the Kremlin says will allow it to focus on seizing the parts of the Donetsk and Luhansk regions, collectively known as Donbas, that remain under Ukrainian control.

While Ukrainian officials initially called for the evacuation of the Kharkiv region, which includes the country’s second-largest city, the revised guidance Wednesday afternoon called only for organized departures from the districts of Barvinkove and Lozova that are on the path of a likely Russian offensive toward Donbas. Kharkiv’s Mayor Ihor Terekhov said in an address that there is no need for anyone to abandon the city, and that he and his entire team are remaining at their workplaces.

In the besieged city of Mariupol, the second-largest in Donbas, Mayor Vadym Boychenko said on Telegram that Russian troops that are engaged in fierce urban combat with Ukrainian defenders have started using mobile crematoriums to dispose of the bodies of Ukrainian civilians. Mr. Boychenko, who put the death toll at 5,000 civilians last week, said he now believes tens of thousands of Mariupol residents could have been killed. There was no independent confirmation of his assessment.

As heavy clashes continued in and near Donbas, Russia pressed on with its campaign of long-range missile strikes, targeting fuel depots across Ukraine and an industrial facility in the eastern city of Novomoskovsk, local officials said. The clashes in the east and south contrasted with the north, where a Russian withdrawal has led to the return of relative normalcy.

European Union member states on Wednesday backed Brussels’ latest proposal, presented Tuesday, for a ban on Russian coal imports, and formal approval is expected by Friday.

White House officials confirmed the Biden administration was implementing full blocking sanctions on Russia’s largest financial institution, Sberbank, and its biggest private bank, Alfa Bank, as well as expanding other economic sanctions, including on Russian President Vladimir Putin’s

daughters and family members of other top officials. In addition, President Biden on Wednesday signed an executive order that includes a prohibition on new investment in Russia by American investors, including those outside the U.S.

U.S. allies are planning to release nearly 60 million additional barrels of oil from their reserves, officials familiar with the matter said, in an effort to tame prices amid Russia’s invasion of Ukraine. Washington previously said it would release 180 million barrels of oil over six months.

Turkey, which has supplied Ukraine with weapons such as Bayraktar TB2 armed drones while also maintaining close relations with Russia, became the first major nation to send diplomats back to Kyiv now that it is no longer under threat of being shelled or overrun. Turkey served as the venue for the latest round of peace talks between Russia and Ukraine, and is involved in efforts to transport civilians and wounded soldiers by sea from Mariupol.

People fleeing fighting in Ukraine arrived at a refugee center in Zaporizhzhia, northwest of Mariupol, on Wednesday.

Photo: bulent kilic/Agence France-Presse/Getty Images

A woman walked past a church Wednesday that was damaged during shelling in the eastern Ukrainian town of Derhachi, near Kharkiv.

Photo: THOMAS PETER/REUTERS

The Turkish Embassy, which had relocated to the western Ukrainian city of Chernivtsi, reopened in Kyiv and will resume consular services, it said on social media. The U.S., by contrast, currently doesn’t have any diplomatic presence on Ukrainian soil, with embassy staff operating from Poland. Several Western leaders have visited Kyiv to show solidarity in recent weeks, including European Parliament President Roberta Metsola

and the prime ministers of Poland, the Czech Republic and Slovenia. Lithuania is planning to send its ambassador back to Kyiv as soon as Thursday, according to Lithuanian officials. Other European nations are likely to follow suit as soon as next week, a Western diplomat said.

Western officials say the withdrawal of Russian forces from around Kyiv is largely complete and that the Ukrainian capital is unlikely to be directly attacked for the foreseeable future as the Russian military refocuses on the Donbas region.

Those officials estimate that around 29 of Russia’s 125 battalion tactical groups have been rendered inoperable following weeks of intense fighting. These units will need to undergo repairs and replenish personnel losses before being redeployed to eastern Ukraine, a process that officials say could take up to a month.

Jens Stoltenberg, secretary-general of the North Atlantic Treaty Organization, said the war was entering a critical phase as Russia prepares for its offensive to take Donbas.

Russia’s withdrawal from northern Ukraine will allow Moscow to focus on seizing the entirety of Donbas and trying to encircle the large Ukrainian military contingent there. Heavy battles continued Wednesday south of the eastern Ukrainian city of Izyum, in the Kharkiv region, as Russian forces attempted to break through and link up with Russian troops trying to push north from Mariupol. Three Ukrainian civilians died Wednesday in shelling in the town of Balakliya near Izyum, local officials said. Four others were killed in Russian shelling in the town of Vugledar in the Donetsk region, according to the regional administration.

Russia in February recognized the so-called Donetsk and Luhansk People’s Republics, proxy statelets that were established through Moscow’s intervention in 2014, as independent. Their claimed borders include two-thirds of the Donetsk and Luhansk regions that were controlled by Kyiv before the war began.

An apartment building in Borodyanka, Ukraine, on Wednesday.

Photo: Efrem Lukatsky/Associated Press

Ukrainians built a new bridge next to a damaged one Wednesday near Irpin, a town on the outskirts of Kyiv recently recaptured from Russian forces.

Photo: oleg petrasyuk/Shutterstock

“The enemy’s main effort is on preparing an offensive to establish full control over the Donetsk and Luhansk regions,” Ukraine’s General Staff said Wednesday. Ukrainian forces in the southern Kherson region have seized four villages, pushing Russian forces further away from the major city of Kryvyi Rih, President Volodymyr Zelensky’s hometown, the military added.

The mayor of the town of Rubizhne in the Luhansk region, where some neighborhoods have been seized by Russian forces, has switched sides and is now working with the occupation forces, the regional government said. The mayor, Serhii Khortiv, released a video repeating Russian propaganda points about the war. In another area under Russian control, the town of Vovchansk in the Kharkiv region, the mayor was filmed under Russian detention saying “Glory to Russia,” according to videos released by pro-Kremlin social-media channels.

Overnight, Russia carried out a series of missile strikes, once again targeting fuel depots as it sought to deprive Ukrainian forces of fuel. Ukrainian demining teams, meanwhile, continued removing unexploded ordnance, land mines and booby traps left behind by Russian forces in the liberated areas, including the town of Bucha, where discoveries of mass graves and bodies in the street after the withdrawal of Russian forces have prompted allegations of war crimes.

Pope Francis on Wednesday deplored the killing of civilians in Ukraine, particularly in Bucha. During his weekly public address at the Vatican, he held up a tattered Ukrainian flag from Bucha and kissed it.

“Ever more horrendous cruelties, even against civilians, women, and helpless children. They are victims whose innocent blood cries out to heaven and implores,” the pope said.

Pope Francis has repeatedly called for an end to the war and lamented the suffering of Ukraine, though he hasn’t named Russia as the aggressor.

Bodies awaiting burial Wednesday in the Kyiv suburb of Bucha, Ukraine.

Photo: Rodrigo Abd/Associated Press

Mr. Zelensky on Wednesday told Irish lawmakers that the strikes on fuel facilities just as Ukrainian farmers start the spring sowing season aim to destroy the country’s civilian infrastructure and cause widespread hunger.

“For them, hunger is also a weapon, a weapon against us ordinary people as an instrument of domination,” he said in an address to members of Ireland’s Parliament, the latest in a series of speeches to international legislatures.

Mr. Zelensky said the food shortages caused by Russian attacks on Ukrainian agriculture and its blockade of the country’s ports would be felt around the world, and particularly in North Africa, which has traditionally relied on Ukrainian wheat.

“There will be a shortage of food and prices will go up,” he said. “This is reality for millions of people who are hungry and it will be more difficult for them to feed their families.”

As the Russian army withdrew from the north to focus on the east, a senior commander characterized the move as the end of a successful phase in its combat operations. Col. Gen. Aleksandr Lapin, the commander of Russia’s Central Military District, said during a medal-awarding ceremony that the first phase of what Moscow calls its special military operation had been successfully completed.

“Soldiers, sergeants and officers demonstrated resilience, courage and valor in completing their mission,” said Gen. Lapin, as Russian officials continued to deny accounts of a massacre of Ukrainian civilians in towns near Kyiv that were occupied by Russian forces until last week.

Mr. Zelensky addressed the United Nations Security Council on Tuesday, saying Russia should be removed from it or it should be dissolved, after warning that newly uncovered atrocities following the withdrawal of Russian forces near Kyiv could be worse than those in Bucha.

“It is difficult to find a war crime that the occupiers have not committed,” Mr. Zelensky said during a virtual appearance at the council’s chamber in New York.

U.S. Attorney General Merrick Garland said the Justice Department was helping foreign prosecutors gather evidence of possible war crimes in Ukraine.

“We have seen the dead bodies of civilians, some with bound hands, scattered in the streets. We have seen the mass graves,” Mr. Garland said on Wednesday. “The world sees what is happening in Ukraine. The Justice Department sees what is happening in Ukraine.”

—Max Colchester and Gordon Lubold contributed to this article.

A man mourned at the grave of a friend in Bucha on Wednesday.

Photo: ALKIS KONSTANTINIDIS/REUTERS

Write to Yaroslav Trofimov at yaroslav.trofimov@wsj.com