(CNN) -- Opposition demonstrators smashed out windows and doors of a government building in Kiev and were using fireworks to smoke out police, according to a journalist at the scene Saturday in the Ukrainian capital.
Opposition leaders said the demonstrators targeted the Ukrainian House because police were launching attacks against them from there, according to the journalist, Victoria Butenko.
The increase in action comes after verbal clashes between Ukraine's president and opposition leader Vitaly Klitschko on Saturday.
On Saturday, President Viktor Yanukovych offered government posts to Klitschko and another leader of an opposing party, the presidential website said.
Klitschko then announced the rejection of those offers on a public stage, where he was joined by heads of other political parties. Klitschko leads the Ukrainian Democratic Alliance for Reforms party (UDAR) and plans to run for president in 2015.
Arseniy Yatsenyuk, who heads the Fatherland Party, would have become the prime minister and, under the president's offer, would have been able to dismiss the current government, which has been one of the protesters' demands.
The president also offered the post of deputy prime minister on humanitarian issues to Klitschko, a champion boxer known as "Dr. Ironfist." The president also said he would agree to a working group to look at changes to the constitution, according to the president's website.
But Klitschko's announcement rejected all parts of the offer, which came after a day of tension between police and hundreds of protesters who continued their vigil in Kiev's Independence Square and surrounding streets.
They have set up tent cities and put up barricades. Large plumes of black smoke billowed from the barricades as riot police watched and waited nearby.
Protests against the government began in November when Yanukovych refused to sign a trade agreement with the European Union in favor of stronger economic ties with Russia.
UDAR warned earlier Saturday that authorities are preparing to provoke peaceful protesters and may plant aggressors among the crowds in an effort to enact emergency rule.
"We call on all Ukrainian citizens not to succumb to provocations of authorities and continue the protest exclusively in a peaceful manner," a party statement said.
A group of protesters blocked the entrance to the Energy Ministry on Saturday, a move Energy Minister Eduard Stavytsky called a direct threat to the entire energy system. Some protesters entered the building and argued with Stavytsky.
"Your action is illegal," Stavytsky told them. "You have crossed the red line. You have entered a high security building."
The protesters left the building saying they did not intend to undermine the work of the ministry in any way.
The European Union is getting involved in the crisis. Next week, EU foreign policy chief Catherine Ashton and a European Parliament delegation are scheduled to visit Ukraine.
Ukraine's richest oligarch, Rinat Akhmetov, issued a statement Saturday saying business cannot keep silent when people are killed.
"A real danger of breakup of the country emerges when a political crisis can lead to a deep economic recession, and thus inevitably result in lower standards of living," he said.
Police say one officer was killed and another one stabbed in clashes with protesters.
CNN's Diana Magnay, Joseph Netto, Victoria Eastwood and journalist Victoria Butenko contributed to this story