The 1.02 million includes 120,000 foreigners and people evacuated from Russian-backed breakaway regions of Ukraine, the so-called Donetsk and Luhansk People's republics, which Russia recognised as independent just before launching its attacks.
According to data from the United Nations, more than 5.4 million people have fled Ukraine since the start of the attacks.
Lavrov, in comments to China's official Xinhua news agency published on the Russian foreign ministry's website, said 2.8 million people in Ukraine have asked to be evacuated into Russia.
Ukraine has said that Moscow has forcefully deported thousands of people to Russia.
Efforts to evacuate civilians from some front-line areas, including the besieged southern port of Mariupol, have repeatedly broken down, with each side blaming the other. read more
Lavrov said that if the United States and NATO are "truly" interested in resolving the Ukrainian crisis, they should stop sending weapons to Kyiv.
"By publicly expressing support for the Kyiv regime, the NATO countries are doing everything to prevent ending of the operation through political agreements," Lavrov said.