MOSCOW — Kyrgyzstan has essentially reversed a decision to close an American air base that is central to the NATO mission in nearby Afghanistan, after the United States acceded to sharply higher rent and to minor restrictions on the site, Kyrgyz and American officials said Tuesday.

The turnabout is a victory for the Obama administration as it seeks to step up operations to quell the Taliban insurgency in Afghanistan. The Kyrgyz government had ordered the base closed in February, apparently under pressure from the Kremlin, which has resented the deep American military presence in an area of the world that it has long considered its zone of influence.

The Manas Air Base in Kyrgyzstan has been used since 2001 as a refueling stop and transit hub for operations in Afghanistan. Thousands of personnel and roughly 500 tons of cargo pass through the base each month.

It has also been a focal point in the struggle between the United States and Russia for influence in the countries of the former Soviet Union. Russia pledged a $2 billion loan to Kyrgyzstan on the day in February that the Kyrgyz president announced that the United States would be evicted from the base.