Updated

At least two people died Wednesday as Ukrainian police clashed with protesters in the latest round of street fighting in the country's capital, Kiev.

The two people whose bodies were found Wednesday near the site of clashes with police, raising fears that their deaths could further fuel violence on the streets of the Ukrainian capital after two months of largely peaceful protests.

Medics at the site said a third man also died after he fell from a high point near a sports arena at the site of clashes, but Natalia Vishnevska, spokeswoman for the city health department, said that man survived the fall and was being treated in the hospital.

The deaths fueled fears that daily protests aimed at bringing down the government over its decision to shun the European Union for closer ties to Moscow and over human rights violations could escalate and turn even more violent.

Prosecutors said the two men were shot with live ammunition, and have opened a criminal investigation to determine who was responsible.

One of the victims has been identified by opposition leaders and doctors treating protesters as Sergei Nigoyan, a 20-year-old ethnic Armenian who came from the eastern city of Dnipropetrovsk in early December to join the protests on Kiev's Independence Square, known as the Maidan.

Prime Minister Mykola Azarov said the police did not have live ammunition and charged that opposition leaders should be held responsible for the deaths.

The three main opposition parties, meanwhile, issued a statement blaming President Viktor Yanukovych and his staunch ally, Interior Minister Vitali Zakharchenko, for the deaths.

Opposition leaders issued a stark ultimatum to President Yanukovych Wednesday to call early elections within 24 hours or face more popular rage.

They demanded that Yanukovych dismiss the government, call early elections and scrap harsh anti-protest legislation. It was last week's passage of the laws cracking down on protests that set off the violent clashes.

"You, Mr. President, have the opportunity to resolve this issue. Early elections will change the situation without bloodshed and we will do everything to achieve that," opposition leader Vitali Klitschko told some 40,000 people who braved freezing temperatures on Kiev's Independence Square late Wednesday.

If Yanukovych does not concede, "tomorrow we will go forward together. And if it's a bullet in the forehead, then it's a bullet in the forehead, but in an honest, fair and brave way," declared another opposition leader, Arseniy Yatsenyuk

The mass protests erupted after Yanukovych spurned a pact with the European Union in favor of close ties with Russia, which offered him a $15 billion bailout. They swelled to hundreds of thousands after a small peaceful rally was violently broken up by police. Seeing the government ignore their demands and opposition leaders unable to present a coherent plan or even select a single leader, radical protesters have clashed with riot police in Kiev since Sunday.

The deaths came on the fourth day of violent street battles between protesters hurling fire bombs and stones and police firing back with tear gas, stun grenades and rubber bullets. The bodies were found before police moved to tear down protesters barricades near official buildings in central Kiev and chased demonstrators away.

Helmeted riot police moved in on hundreds of protesters, dismantling the barricades, beating many with truncheons and firing shots at some. One man was attacked by more than a dozen policemen, was made to take off his winter jacket and dragged away, where he was reportedly beaten again.  Dark smoke from burning tires billowed in the air and an armored vehicle was seen near police lines.

The police drove demonstrators down a hill toward the main protest site on Independence Square, where protesters have set up an extensive tent camp and rallied around the clock since November. There was no immediate police move on the main camp.

Oleksandr Turchynov, one of the opposition leaders, called on Ukrainians to rush to the center of Kiev to defend their country. "Ukraine will not be a dictatorship, it will be an independent, European country. Let us defend Ukraine!"

The U.S. Embassy said it was revoking the visas of some Ukrainian officials linked to the violence and was considering further action. The embassy would not name the officials, citing privacy laws. The EU condemned the violence and said it was also considering action against the Ukrainian government.

After several days of refusing face-to-face talks, Yanukovych met Wednesday with three main opposition leaders to negotiate a solution.

The protests were the biggest since the peaceful 2004 Orange Revolution, which annulled Yanukovych's fraud-tinged victory in a presidential vote and forced a new vote that brought his pro-Western rival to power. The current protests were also largely peaceful for nearly two months, but turned violent after Yanukovych, elected in 2010, pushed through sweeping anti-protest legislation and ignored all the protesters' demands. The deaths mark a turning point in the standoff that could lead to more violence.

"Look, the deaths and the injuries speak to the actions of those in power. They've crossed the line," said Andriy Kolosovich, 20, who was injured by a stun grenade and was being treated for leg injuries in a nearby medical unit set up by protesters.

The police move on the barricades came on the same day when much of international attention was focused in Switzerland, where peace talks aimed at ending Syria's war began Wednesday.

The Associated Press contributed to this report.