During a visit to Hungary, Lavrov said the United States is trying to convince "several Central Asian countries" to take in Afghans who previously worked with US forces in the now Taliban-controlled country.
He alleged that Washington tells the countries the Afghans will only be there temporarily.
"They say it's for a few months because they need time to make them visas," Lavrov said at a press conference with his Hungarian counterpart in Budapest.
"Afghans who worked with US forces were probably security checked inside out. Why do you need two more months to give these people a visa?" he asked, accusing the United States of a lack of respect for Central Asian nations.
Around 1,500 Afghans have crossed into neighbouring Uzbekistan after the Taliban takeover and are living in tents near the border, according to the Afghan embassy in Tashkent.
Lavrov's comments come after Russian leader Vladimir Putin complained last week about Western countries trying to place Afghan refugees in Central Asian countries "before obtaining visas to the United States or other countries."
Putin has warned against an influx of refugees from Afghanistan, saying militants could enter Russia under the guise of seeking asylum.
Several former Soviet republics in Central Asia share a border both with Afghanistan and Russia, allowing potential militants to reach the country, he told officials on Sunday.
Moscow has been cautiously optimistic about the new leadership in Kabul.
The Kremlin said Tuesday it was "attentively watching" the "disagreements" on whether to extend an August 31 deadline for the complete withdrawal of US troops from Afghanistan.
