Russian President Vladimir Putin, during a June 16 summit meeting with President Biden, objected to any role for American forces in Central Asian countries, senior U.S. and Russian officials said, undercutting the U.S. military’s efforts to act against new terrorist dangers after its Afghanistan withdrawal.

The previously unreported exchange between the U.S. and Russian leaders has complicated the U.S. military’s options for basing drones and other counterterrorism forces in countries bordering landlocked Afghanistan. That challenge has deepened with the collapse over the weekend of the Afghan government and armed forces.

The Taliban seized control of Afghanistan more rapidly than intelligence officials expected. Here’s a look at the nine days that sealed the group’s yearslong takeover. Illustration: Laura Kammermann The Wall Street Journal Interactive Edition

The exchange also indicates that Moscow is more determined to try to maintain Central Asia as a sphere of influence than to expand cooperation with a new American president over the turmoil in Afghanistan, former and current U.S. officials said.

“The Russians have no interest in having the U.S. back in there,” said Paul Goble, a former State Department expert on Eurasia.

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The U.S. requirement for what the Pentagon calls an “over-the-horizon” counterterrorism capability in Afghanistan has grown substantially in recent days with the Taliban takeover.

Without access to Central Asian nations, such as Uzbekistan, Kyrgyzstan or Tajikistan, the U.S. would need to rely on bases in Qatar, other Arab Gulf states and U.S. Navy aircraft carriers in the Indian Ocean to fly aircraft to Afghanistan. Flight times from the Gulf states are so long that a U.S. drone might spend more than 60% of its mission flying to and from Afghanistan from the U.S. base at Al Udeid, Qatar, a former senior U.S. military official said. This would limit the time for conducting reconnaissance or carrying out strikes over the country.

Mr. Putin told Mr. Biden at their Geneva meeting, however, that Moscow was opposed to any U.S. military role in the Central Asian region and that China would reject it as well—a position a senior Russian official reiterated this week. A senior U.S. official said the Russian president emphasized the point even though Mr. Biden didn’t seek Mr. Putin’s support for positioning U.S. military or intelligence assets in the area.

“We do not see how any form of U.S. military presence in Central Asia might enhance the security of the countries involved and/or of their neighbors. It would definitely NOT be in the interests of Russia,” Russian Deputy Foreign Minister Sergei Ryabkov wrote Thursday in a statement emailed to The Wall Street Journal. “This position has not changed against the backdrop of what is transpiring in Afghanistan these days.”

Even maintaining the capability to continue flights from the Gulf region is not without potential diplomatic complications, now that the Taliban control Afghanistan, former officials said.

The U.S. used bases in Uzbekistan and Kyrgyzstan during the early phase of its operations in Afghanistan. But the U.S. left Uzbekistan in 2005 and Kyrgyzstan nearly a decade later after Russia and China pressured countries in the region to curtail their military cooperation with Washington.

Because of its proximity to Afghanistan, Central Asia has been eyed by the U.S. military as a potential hub for conducting drone reconnaissance or drone strikes against terrorist groups in the country. Adding to the humanitarian and diplomatic challenges for Washington, the Taliban offensive has led Afghan refugees and even Afghan military warplanes and helicopters to seek refuge in Central Asian states.

Uzbekistan law, however, doesn’t allow the foreign military bases on its territory, and there has been no indication the Uzbekistan government is ready to change its position. Officials from Kyrgyzstan, Tajikistan and China didn’t immediately respond to a request for comment.

In July, Elizabeth Sherwood-Randall, the top White House official for homeland security, led a U.S. delegation to an international conference in Tashkent, Uzbekistan, to discuss possible counterterrorism cooperation and other foreign policy issues, the White House said then.

That same month, Secretary of State Antony Blinken and Defense Secretary Lloyd Austin met in Washington with Uzbekistan Foreign Minister Abdulaziz Kamilov and Tajikistan Foreign Minister Sirojiddin Muhriddin.

U.S. Secretary of State Antony Blinken, right, and Uzbekistan Foreign Minister Abdulaziz Kamilov at the State Department in Washington, last month.

Photo: ken cedeno/Reuters

While Russia has considerable influence in Central Asia, former U.S. officials said Moscow doesn’t necessarily call the shots in some of the region’s capitals.

“Moscow has some leverage, but the leverage is not absolute,” said Mr. Goble. “If you ask me, would Tashkent like to cooperate with the United States, the answer is ‘yes.’ Would Moscow like the United States and Tashkent to be cooperative, the answer I think is ‘no.’”

The chaos that engulfed Afghanistan has added pressure to advance cooperation with Central Asian states. In June, Chairman of the Joint Chiefs Gen. Mark Milley told Congress there was a “medium” risk that terrorist groups could reconstitute themselves in Afghanistan in about two years. On Sunday, however, Gen. Milley indicated in a telephone briefing with senators this timetable could be shorter.

Moscow has been mounting its own diplomatic efforts in public comments and private messages to Central Asian officials. Its goal has been to forestall a U.S. military foothold in the region for counterterrorism, a senior U.S. government official said.

In recent weeks, Russia held a series of joint war games with troops from Tajikistan, where it has a military base, and Uzbekistan, underlining its pledge to assist the region in countering any security threats from Afghanistan. The drills, which involved 2,500 troops from the three nations and some 500 military vehicles, were held close to the Afghan border and included Russian planes striking mock militant camps.

Russian troops are seen during joint military exercises by Russia, Tajikistan and Uzbekistan at Tajikistan’s Harb-Maidon military training ground, about 12 miles from the Afghan border.

Photo: Nozim Kalandarov/Zuma Press

“If the logic of the United States is that its military presence might enhance security of Central Asia, the natural response for Moscow is that we can take care of it, we have done it for a long period of time,” said Andrey Kortunov, director general of the Russian International Affairs Council, a nonprofit think tank in Moscow.

A decade ago, Russia and the U.S. cooperated over Afghanistan. In 2009, the U.S. arranged to send supplies to Afghanistan via Russia and Central Asia nations because of difficulties in resupplying troops through Pakistan. The arrangement was known as the Northern Distribution Network. During the years those logistics routes were operating, the U.S. had as many as 100,000 troops in Afghanistan, and Russia had an interest in having American and allied forces fight Islamic militants.

“Then there was a perception that the U.S. was going to stay in Afghanistan and try to fix things,” said William Courtney, a former U.S. ambassador to Kazakhstan and Georgia. “But now we have been humbled. They don’t believe that we will be reliable protectors against Taliban influence in Central Asia. Their main concerns are Islamic radicals coming north and narcotics coming north.”

—Georgi Kantchev in Moscow contributed to this article.

Write to Michael R. Gordon at michael.gordon@wsj.com