Pro-Russian separatists in Ukraine say they are ready for a cease-fire with the government amid gains by Ukrainian forces against the rebels.
Kyiv has not yet responded to the rebel offer. But the government has said it could agree to a cease-fire if the separatists give up their weapons.
The Ukrainian military is continuing to squeeze separatist forces in their remaining strongholds of Donetsk and Luhansk.
Conditions in Donetsk have been deteriorating, raising concerns of a humanitarian crisis in the city. A senior Ukrainian government official says Russian forces had wanted to enter Ukraine under the guise of a humanitarian mission, but Ukraine blocked the move. Russian officials deny this.
Also Saturday, U.S. Vice President Joe Biden discussed the situation in eastern Ukraine with Ukrainian President Petro Poroshenko by telephone. A White House statement said the two stressed that any Russian action, even for "purported humanitarian purposes" would violate international law and be unacceptable without the consent and authorization of Kyiv.
According to the statement, Poroshenko added that he is in contact with the Red Cross about the distribution of humanitarian aid, including assistance from the United States, to eastern Ukraine.
The White House said the two men also agreed that if Russia wants to improve the humanitarian situation in eastern Ukraine, it must stop shelling Ukrainian troops, release Ukrainian hostages being held in Russia and stop supporting pro-Russian separatists.
A U.S. State Department official says Secretary of State John Kerry spoke by telephone Saturday with Russian Foreign Minister Sergei Lavrov.
The official says Kerry made it clear that the best way to get humanitarian aid into Ukraine is through international organizations that are already on the ground. Kerry told Lavrov that Russia should not intervene in Ukraine under the pretext of peacekeeping or humanitarian convoys.
The White House says President Barack Obama and German Chancellor Angela Merkel agreed by phone Saturday that any Russian intervention in Ukraine without Kyiv's consent would violate international law and bring additional consequences.
The U.S. ambassador to the United Nations, Samantha Power, told a Security Council meeting on Ukraine Friday that while Russia has proposed creating humanitarian corridors to send aid to civilians in the war-torn region, such aid should be delivered by international organizations.
Both U.S. and NATO officials said Moscow had recently increased the number of its troops along the Ukrainian border to around 20,000.
Power also said Friday that Russian cross-border military assistance to separatists in eastern Ukraine has increased substantially in recent weeks, and that new separatist fighters are being trained on Russian soil.