Russian President Vladimir Putin on Sunday said that the situation in Afghanistan directly affects Russia's security, according to RIA news agency.
Russia does not want Afghan militants arriving under the cover of refugees, Putin added.
Putin criticized the idea of some Western countries to relocate refugees from Afghanistan to neighboring Central Asian countries while their visas to the United States and Europe are being processed.
"Does that mean that they can be sent without visas to those countries, to our neighbors, while they themselves (the West) don't want to take them without visas?" TASS news agency quoted Putin as telling leaders of the ruling United Russia party.
"Why is there such a humiliating approach to solving the problem?" he said.
Putin said Russia, which allows visa-free travel for residents of ex-Soviet Central Asian countries, opposes that.
"We don't want militants showing up here under cover of refugees," TASS cited Putin as saying.
While some Western nations scrambled to evacuate people from Afghanistan, Moscow praised the Taliban for restoring order following its takeover of the country.
Russian Foreign Minister Sergei Lavrov said Taliban leaders had stuck to their promises so far.
"We are seeing the statements the Taliban made about ceasing combat actions, an amnesty for all of those involved in the confrontation, about a need for a nationwide dialogue ... they are being implemented," he was cited by RIA as saying.
Lavrov said the Taliban had started contacts with former Afghan President Hamid Karzai.