Standing alongside acting Ukrainian Prime Minister Arseniy Yatsenyuk, 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."
Biden said Russia needs to act "without delay," adding, "We will not allow this to become an open-ended process."
Yatsenyuk was harsher in his characterization 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 from both leaders demonstrated the fragility of last week's multinational agreement.
Biden also announced the United States will provide an additional $50 million to help Ukraine's beleaguered government with political and economic reforms.
The money includes $11 million to help conduct the May 25 presidential election, including voter education, administration and oversight. It also will help fund expert teams from U.S. 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 $8 million in nonlethal military assistance for the Ukrainian armed forces, including bomb-disposal equipment, communications gear and vehicles.
In the most high-level visit of a U.S. official since the crisis erupted, Biden met privately with Yatsenyuk and acting Ukrainian President Oleksandr Turchynov. He also met with democracy activists and spoke to TV cameras to tell the people of eastern Ukraine he had urged the nation's leaders to keep reaching out to them.
"I know the men and women who hide behind masks and unmarked uniforms, they do not speak for you," he said. "All are welcome as equals in shaping a new Ukraine. We count on you to be the voice for rights and freedoms."
Earlier, he 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," Biden said. "And we want to be your partner, your friend in the project. And we're ready to assist."
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. Biden told the candidates he hopes that they have more luck than he did in two presidential runs.
Sen. John McCain, who recently visited the region, described U.S. allies in Eastern Europe as "extremely nervous" about the intentions of Russian President Vladimir Putin. In an MSNBC interview, the Arizona Republican called on Obama to give the Ukrainian government "some weapons to defend themselves."
McCain, the ranking Republican on the Senate Armed Services Committee, said America must show more support for countries under siege. That doesn't mean the United States "must fight" every war, he said, but "the only thing that Putin understands is a strong, viable alliance."
Biden's 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 Kyiv.
"You face very daunting problems and some might say humiliating threats that are taking place indirectly," Biden told the Ukrainian lawmakers.
He said the United States is an example of people from different cultures united as one nation, although he said Ukraine has a big difference. "We're not sitting against a border of another powerful nation," Biden said.
Biden told the lawmakers a priority for the U.S. is to help them become independent from Russian energy supplies. "Imagine where you'd be today if you were able to tell Russia, 'Keep your gas,'" Biden said. "It would be a very different world you'd be facing today."
Biden said they have an historic chance now that former President Viktor Yanukovych has fled the country.
"This is a second opportunity to make good on the original promise made by the Orange Revolution," Biden said in a reference to 2004 protests that overturned a widely criticized election that had given Yanukovych the presidency. Yanukovych later took office but left the country after violent protests in February.
Biden added, "To be very blunt about it, and this is a delicate thing to say to a group of leaders in their house of parliament, but you have to fight the cancer of corruption that is endemic in your system right now." He mentioned reforming the courts and finding the right balance of power between the president and Rada.
"I want you to know I do not underestimate the incredible pressure you all are under," Biden said. "I do not underestimate the challenge that you all face. And I do not underestimate the frustration you must feel when someone like me comes along and says this is a great opportunity for you."
But he added that the upcoming election may be the most important in the country's history. "The truth of the matter is your fellow countrymen expect a whole lot of you right now," he said.
Follow Nedra Pickler on Twitter at https://twitter.com/nedrapickler