Yanukovych said he believed an amnesty should be declared for those arrested in the protests "in order to give guarantees that the process of confrontation will stop."
"I am outraged by the radical actions on both sides ... from the side of provocateurs and from the side of the security forces, which have not always behaved properly," he added.
Also looming in the crisis is continued anxiety about a Tuesday meeting between Yanukovych and Russian President Vladimir Putin.
Russia strongly opposes Ukraine's closer ties with the EU and wants it to join a customs union, also including Belarus and Kazakhstan, which opponents denounce as effectively a reconstitution of the Soviet Union. Concern persists that Yanukovych could agree to join the customs union on Tuesday.
Prime Minister Mykola Azarov said Friday the presidents are expected to sign agreements resolving "the overwhelming majority of trade disputes" with Russia, but did not mention the customs union.
On Thursday, after meeting with EU officials in Brussels and receiving promises of more aid from the bloc, Deputy Prime Minister Serhiy Arbuzov said Ukraine aims to sign the trade and political pact with the EU soon, once unspecified issues are worked out.
The opposition was dismissive.
"They had a chance to sign just two weeks ago and why hasn't that happened? It is just a game," Klitschko said.
The economically troubled nation of 46 million is divided over the EU deal. Many people in eastern Ukraine, the country's industrial heartland and Yanukovych's support base, are against the protesters in Kiev and want the country to have closer economic ties with Russia.
Associated Press writer Dalton Bennett contributed to this report.