U.S. warns Russia not to intervene in Ukraine under 'peacekeeping' pretext

(CNN) -- U.S. Secretary of State John Kerry warned his Russian counterpart, Sergey Lavrov, on Saturday that "Russia should not intervene in Ukraine under the guise of humanitarian convoys or any other pretext of 'peacekeeping,'" according to a senior State Department official.

Kerry urged "all parties to work through international organizations" to provide humanitarian assistance in eastern Ukraine, the official said.

In a separate call Saturday, U.S. Vice President Joe Biden and Ukrainian President Petro Poroshenko agreed that any Russian action in Ukraine, even for purported "humanitarian" purposes, without the formal, express consent and authorization of the Ukraine government would be "unacceptable and a violation of international law," according to the White House.

Russia has denied allegations that it is supporting separatists in Ukraine and maintains it wants to see a diplomatic solution to the ongoing crisis there. But U.S. and Ukrainian officials have accused Russia of saying one thing while doing another: increasing troop levels along the border and continuing to send support to pro-Russian separatists.

Pro-Russian separatists say 'fight to the death'

Despite claims by Ukrainian officials, the pro-Russian separtists hold firm that Ukrainian forces "have never been able to take over the Donetsk districts" -- the hotbed of violence in eastern Ukraine.

The self-proclaimed leader of the Donetsk people's republic said on Saturday that pro-Russian separatists would consider a humanitarian cease-fire to bring aid to civilians but they are not ready to surrender their territory and would "fight to the death."

"We are ready for ceasefire to avoid escalation of the humanitarian disaster in Donbass," Alexander Zakharchenko, prime minister of the self-styled Donetsk People's Republic in a statement, said, referring to the populous region that includes Donetsk.

Earlie this month, The United States and European Union increased economic sanctions on Moscow for supporting pro-Russian separatists fighting Ukraine government forces in the eastern regions of Donetsk and Luhansk, along the border with Russia.