Ukraine on Monday rejected Moscow's offer of humanitarian corridors to Russia and Belarus, Deputy Prime Minister Iryna Vereshchuk said.
"This is not an acceptable option," she said, after Russia proposed safe passage for civilians from Kharkiv, Kyiv, Mariupol and Sumy.
The civilians "aren't going to go to Belarus and then take a plane to Russia."
The Russian army said earlier on Monday it was opening humanitarian corridors from the four Ukrainian cities.
Russian army spokesman Igor Konashenkov said local ceasefires had begun at 07:00 GMT to allow civilians to escape.
Fighting was still ongoing Monday in the four cities — the capital Kyiv, the second city Kharkhiv in the east, the southeastern port of Mariupol on the Sea of Azov and Sumy, near the eastern border with Russia.
But the fact the corridors led into Russia or its ally Belarus raised questions over the safety of those who might use them.
Two recent attempts to allow thousands of civilians to leave the besieged city of Mariupol have ended in disaster, with civilians under fire and both sides accusing each other of violations.
Russian President Vladimir Putin has vowed to "neutralize" Ukraine "either through negotiation or through war," and expectations remain low for a third round of Russian-Ukrainian talks set for Monday.