KIEV, Ukraine (AP) -- About 10,000 anti-government demonstrators angry about Ukraine's refusal to sign a pro-European Union agreement converged Saturday on a square outside a monastery where protesters driven away in a pre-dawn clash with police were taking shelter.
Opposition leaders called for nationwide strikes and for Ukrainians to mobilize en masse. Another big demonstration was called for Sunday.
The demonstrators outside the St. Michael's Golden-Domed Monastery were shouting "shame" and "resign." Some vowed to spend the night on the square, as temperatures hovered only slightly above freezing.
"Each of you have to come out and express your own position on what kind of country you want to live in -- a totalitarian, police-controlled country where your children will be beaten up or in a European country," said Vitaly Klitschko, a world boxing champion and leader of the opposition Udar party.
Klitschko's call encapsulated the two issues agitating the demonstrators: President Viktor Yanukovych's refusal to sign an association agreement with the EU and the violent dispersal of protests denouncing that decision.
Yanukovych said in an address Saturday evening that he condemned "the actions that led to the forceful confrontation and the suffering of people." He called for an investigation and for those responsible to be punished.
"I confirm that we are united in our choice of a common European future," Yanukovych said.
Yanukovych has said he still hopes that Ukraine will one day sign the agreement with the EU, but that the country was too fragile economically and could not afford to sacrifice trade with Russia.
Moscow regards Ukraine as historically part of its orbit and has tried to block the deal with the EU by banning some of Ukraine's imports and threatening more trade sanctions. A 2009 dispute between Kiev and Moscow on gas prices resulted in a three-week cutoff of gas to Ukraine.
The association agreement would have established free trade and deepened political cooperation between Ukraine and the EU, but stopped short of membership in the regional bloc.
In the city of Lviv in western Ukraine, where sentiment for European integration is especially strong, 10,000 demonstrators protested the failure to sign on Saturday.
Meanwhile, another prominent protest figure, parliament deputy Arseniy Yatsenyuk, is calling for Yanukovych to be impeached and on his government to resign. Yatsenyuk said opposition leaders were working to organize nationwide strikes.
Early Saturday, officers in riot gear moved against several hundred protesters at Independence Square in the Kiev city center, beating some with truncheons. Some protesters then went to the monastery about 500 meters away to take shelter in its cathedral.
In the early morning action, police took 35 demonstrators into custody. Some protesters were bleeding from their heads and arms after the clash.
"It was horrible. We were holding a peaceful demonstration and they attacked us," protester Lada Tromada said. "They threw us away like garbage."
Prime Minister Mykola Azarov said in a statement that "the information from different sides which I have at the moment does not allow firm conclusions about who is responsible for this provocation," but said it would be fully investigated.
Kiev police chief Valery Koryak laid the responsibility on the protesters, saying the police were provoked into taking action, the Interfax news agency reported.
The European Union and the U.S. State Department condemned the violence against the protesters.
"We urge Ukraine's leaders to respect their people's right to freedom of expression and assembly," State Department spokeswoman Jen Psaki said in a statement.
"The European Union strongly condemns the excessive use of force last night by the police in Kiev to disperse peaceful protesters, who over the last days in a strong and unprecedented manner have expressed their support for Ukraine's political association and economic integration with the EU," the EU statement said.
About 10,000 people had rallied on the square Friday evening to protest Yanukovych's backing off from the pact, which had been eagerly anticipated by Ukrainians who want their country of 45 million people to break out of Moscow's orbit and tilt to the West. Opinion surveys in recent months showed about 45 percent of Ukrainians supporting closer integration with the EU and a third or less favoring closer ties with Russia.
Protests had been held in Kiev over the past week since Yanukovych backed away from the EU agreement. It was to have been signed Friday at an EU summit in the capital of Lithuania, and the passing of that date sparked an especially large turnout of protesters.
Saturday's harsh action was in contrast to the mass protests of the 2004 Orange Revolution, when tens of thousands came to the square nightly for weeks and set up a vast tent camp on the main street leading to the square. Police had a mostly low-profile presence during those demonstrations.