Russia will open humanitarian corridors on from Kyiv, Chernihiv, Sumy and Mariupol on March 11, officials have told a news agency.
Mikhail Mizintsev, head of the Russian National Defence Control Centre, said people could either travel to Russia or other cities in Ukraine.
"From 10:00 am Moscow time (0700 GMT) on March 11, 2022, the Russian Federation will declare a 'regime of silence' and is ready to provide humanitarian corridors," Mizintsev said in a statement.
Ukrainian officials complain that Russians have broken the terms of previous agreements while Moscow accuses Ukrainian forces of disrupting the operations.
Not a single civilian was able to leave Mariupol on Thursday as Russian forces failed to respect a temporary ceasefire to allow evacuations, Ukraine's Deputy Prime Minister Iryna Vereshchuk said on national television.
Officials said the Ukrainian side would have to provide lists of people and vehicle registration numbers before the corridors were opened.
Talks between Ukraine and Russia's foreign ministers on Thursday failed to bring any respite in the two-week-old conflict as hundreds of thousands of civilians remained trapped in Ukrainian cities sheltering from Russian air raids and shelling.
The news comes as horrifying pictures of mass graves emerge from the besieged city of Mariupol and reports of a the Russian advance slowing throughout Ukraine.
Moscow violated an expected ceasefire on Wednesday, continuing heavy shelling on Mariupol, raising questions about whether the latest announcement of humanitarian corridors will be respected by forces on the ground.
The Black Sea port city, home to over 400,000 people, has endured days of intense shelling with aid agencies saying humanitarian help is desperately needed as trapped residents are without food, power or water.
This latest announcement, of humanitarian corridors from the embattled urban centres, would allow vital aid to reach civilians trapped inside and allow trapped Ukrainians to flee.
Russia is committing an increasing number of its forces to encircling key cities in Ukraine, slowing its advance through the country, Britain's defence ministry said on Thursday.
The ministry said: "Due to strong Ukrainian resistance, Russian forces are committing an increased number of their deployed forces to encircle key cities.
"This will reduce the number of forces available to continue their advance and will further slow Russian progress."
Chilling photos from besieged Mariupol show corpses being discarded in mass grave sites as the death toll in the city grows.
This week it was revealed more than 1,200 people have died in the port city with authorities ordering workers to dig 25 metre long trenches as morgues are at breaking point.
Forty bodies were dumped in the trench in the cemetery on Tuesday, followed by 30 more on Wednesday. They were said to be both civilians and soldiers.
