The Russian military will hold fire and open humanitarian corridors in several Ukrainian cities including the capital Kyiv on Monday, Russia's defence ministry said.
The corridors, which will also be opened from the cities of Kharkiv, Mariupol and Sumy, are being set up at the personal request of French President Emmanuel Macron and in view of the current situation in those cities, it said.
According to maps published by the RIA news agency, the corridor from Kyiv will lead to Belarus, and civilians from Kharkiv will only have a corridor leading to Russia.
Corridors from Mariupol and Sumy will lead both to other Ukrainian cities and to Russia.
Those who want to leave Kyiv will also be able to be airlifted to Russia, the ministry said, adding that it would use drones to monitor the evacuation and "attempts by the Ukrainian side to deceive Russia and the whole civilised world... are useless this time."
Two planned evacuation operations from Mariupol and the nearby city of Volnovakha have failed over the last two days as the sides accused each other of failing to stop shooting and shelling.
In Mariupol alone, Ukrainian authorities have said they planned to evacuate over 200,000 civilians, or half of the city's population.
According to the Defence Ministry, Russia's military will hold fire after fighting halted the weekend's evacuation efforts.
Russia's invasion has been condemned around the world, sent more than 1.5 million Ukrainians fleeing abroad, and triggered sweeping Western-led sanctions aimed at crippling the Russian economy.
Russia calls the campaign it launched on February 24 a "special military operation". It has repeatedly denied attacking civilian areas and says it has no plans to occupy Ukraine.