Biden's arrival in Kiev comes after a deadly gunfight killed at least two pro-Russian militants, an incident which sparked "outrage" in Moscow.
But the Western-backed authorities in Kiev claimed the violence was a set-up by Russia to create a pretext for it to send in troops.
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The deal, aimed at easing what has become the worst crisis between Russia and the West since the Cold War, now appears to have stalled.
Russia has an estimated 40,000 troops massed on Ukraine's border in what NATO says is a state of readiness to invade, while the United States, according to The Washington Post, is preparing to send ground troops to neighbouring Poland.
Vladimir, a masked 20-year-old pro-Russian rebel, said yesterday's shootout erupted when four cars pulled up to a roadblock manned by the separatists in the early hours.
"We wanted to conduct a check, and then they opened fire on us with automatic weapons," Vladimir said.
Three of the separatists were killed, he added.
An AFP photographer saw two bodies laid out in a truck near the scene.
The identity of the assailants, who escaped before the pro-Russian rebels could bring in reinforcements, was not known.
The leader of the separatists in Slavyansk, Vyacheslav Ponomaryov, said he believed two attackers were also killed.
He declared a midnight-to-6:00 am curfew in Slavyansk, and appealed for Russian President Vladimir Putin to send in troops as "peacekeepers to defend the population against the fascists", the separatists' label for Ukraine's new government and its supporters.
Later, Ponomaryov said, "If you can't send peacekeeping forces, send us weapons."
Putin has said he "very much hopes" he will not have to send his forces into Ukraine, but asserts he has a "right" to do so.
Yesterday, Russia's foreign ministry declared its "outrage" at the deadly attack.
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