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 U.S. has warned that it will quickly order new economic sanctions on Russian officials and entities if Moscow doesn't follow through on the provisions in last week's accord.
Moscow has rejected charges that it was behind the troubles in eastern Ukraine and that it has failed to live up to the Geneva agreement. Officials there have decried "ultimatums" from the West.
"Before putting forth ultimatums to us, demanding fulfillment of something within two-three days or otherwise be threatened with sanctions, we would urgently call on our American partners to fully recognize responsibility for those whom they brought to power and whom they are trying to shield, closing their eyes to the outrages created by this regime and by the fighters on whom this regime leans," Russia's Foreign Minister Sergey Lavrov said.
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."
Biden paid tribute to the protest movement by visiting St. Michael's Golden-Domed Monastery, perched on a hill a few blocks from Kiev's Independence Square that was the site of massive demonstrations against then-President Viktor Yanukovych. The monks provided refuge to protesters fleeing riot police and served as a field hospital to treat demonstrators who were shot in the square. Some died from their wounds beneath the monastery's high, blue bell tower.
"These heroes remind us of the true cost of a better future and the nobility of those who reach for it," Biden said.
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 moldings 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 Kiev. He told the lawmakers a priority for the U.S. is to help them become independent from Russian energy supplies.