Standing alongside acting Ukrainian prime minister Arseniy Yatsenyuk in Kiev, Mr Biden called on Moscow to encourage pro-Russia separatists in eastern Ukraine to vacate government buildings and checkpoints, accept amnesty and "address their grievances politically".
Mr Biden said Russia needs to act "without delay", adding: "We will not allow this to become an open-ended process."
The vice-president also announced the US will provide an additional $50 million (£30m) to help Ukraine's beleaguered government with political and economic reforms.
The money includes $11m (£6.5m) to help conduct the May 25 presidential election . It will also assist fund expert teams from US government agencies to help Ukraine to reduce its reliance on energy supplies from Russia. Other technical advisers will help fight corruption.
The White House also announced $8m (£4.7m) in non-lethal military assistance for the Ukrainian armed forces, including bomb-disposal equipment, communications gear and vehicles.
In the most high-level visit of a US official since crisis erupted in Ukraine, Mr Biden met privately with Mr Yatsenyuk and acting Ukrainian president Oleksandr Turchynov.
Mr Yatsenyuk was harsher in his characterisation of Russia. "No country should be able to behave like an armed bandit," he said. "Russia should stick to its international commitments and obligations. They should not behave as gangsters in the modern century."
The warnings for Russia demonstrated the fragility of the multinational agreement reached last week, whose future is in doubt. Earlier, Mr Biden told leaders from various political parties that he brings a message of support from President Barack Obama as they face a historic opportunity to usher in reforms.
"The opportunity to generate a united Ukraine, getting it right, is within your grasp," Mr Biden said. "And we want to be your partner, your friend in the project. And we're ready to assist."
Mr Biden spoke to nine Ukrainians in a hearing room with gilded mouldings at the parliament, or Rada, as the media looked on.
The group included three candidates running for president in the May 25 election - most notably billionaire chocolate magnate and front-runner Petro Poroshenko. Mr Biden told the candidates he hopes that they have more luck than he did in two presidential runs.
The visit comes at a critical time, days after a tenuous international agreement was reached to de-escalate violence in eastern Ukraine, where pro-Russia insurgents oppose the government in Kiev.
l A Ukrainian military aircraft was hit by gunfire yesterday while on a reconnaissance flight over the eastern pro-Russian held city of Slaviansk. Several bullets struck the Antonov An-30 turboprop spotter plane before it landed safely.