Moscow said on Tuesday (Mar 8) that Ukrainian authorities had endorsed only one civilian evacuation route from areas affected by fighting out of 10 that were proposed, including five towards territory controlled by Kyiv, the Interfax news agency reported.
The Russian defence ministry said 723 people had been evacuated through the Sumy-Poltava corridor, including 576 Indian nationals, in a first convoy.
Ukraine said on Monday that a Russian proposal on humanitarian corridors was "completely immoral" after Moscow suggested it would allow people to flee Ukrainian cities towards only Belarus or Russia.
Civilians have been trapped by fighting since Russian troops invaded Ukraine on Feb 24, and officials say food, water and other supplies have been running low in some cities.
Mikhail Mizintsev, head of the Russian National Defence Control Centre, said on Tuesday that Moscow had proposed evacuation corridors from Kyiv, Chernihiv, Sumy, Kharkiv and Mariupol - "one from each city to the Russian Federation, as well as one each through the territories controlled by the Kyiv authorities to Poland, Moldova, Romania".
Ukrainian civilians did begin leaving the northeastern city of Sumy and the town of Irpin near Kyiv, heading towards the Ukrainian city of Poltava, but Ukraine said Russian forces had shelled another evacuation route - from the port city of Mariupol.
The Russian defence ministry said earlier that Russian forces had introduced a "silent regime" along the evacuation corridors from 0700 GMT, Interfax reported.