The window for a resolution to the crisis was closing quickly and may already have closed, Biden warned Yanukovych, according to a senior administration official familiar with the conversation.
Yanukovych was initially defiant, the official said, and accused the protesters in the streets of Kiev of being terrorists.
Though Yanukovych became less resistant to Biden's appeals as the call continued, the vice president hung up the phone uncertain of the embattled leader's next move.
On Friday, Yanukovych agreed to form a new government and hold an early election. Ukraine's parliament slashed the president's powers and voted to free his rival, former Prime Minister Yulia Tymoshenko, from prison. And on Saturday, Yanukovych fled Kiev, reportedly holing up in Crimea, a pro-Russian area of Ukraine.
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The tenuous political agreement was orchestrated by European diplomats, with the US and Russia playing supporting roles.
Biden, who had built a working relationship with Yanukovych since becoming vice president, was at the forefront of the delicate diplomatic manoeuvring for the Obama administration.
The vice president also met throughout the crisis with Ukrainian religious leaders and Ukrainian-American groups, according to the administration official, who was not authorised to discuss the vice president's involvement by name and insisted on anonymity.