The two-hour, pre-dawn confrontation came after Yanukovich made his biggest concession yet in a two-month-old standoff that has cast Ukraine into crisis, killed at least three people and deepened tension between Russia and the West.
Yanukovich abruptly abandoned plans to sign political association and free trade deals with the European Union in November, pledging instead to improve ties with former Soviet master Russia and angering millions who dream of being in Europe.
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Hoping to end protests that threaten to bring the country to a standstill, Yanukovich on Saturday offered former economy minister Arseny Yatsenyuk the post of prime minister. Klitschko, a former international boxing champion, was offered the post of deputy prime minister responsible for humanitarian issues, a statement on the presidential website said.
The presidency linked its offer to the opposition reining in violent protesters. Though the protest movement is largely peaceful, a hard core of radicals have been fighting pitched battles with police away from Independence Square.
Opposition leaders, whose power base is among protesters massing in the square whose name evokes the independence Ukraine gained in 1991, continued to press for concessions including early elections and the repeal of an anti-protest law.
"We are ready to take on this responsibility and take the country into the European Union," Yatsenyuk was quoted as telling crowds on Independence Square after emerging from talks with Yanukovich. But he added this would entail the freeing of former prime minister Yulia Tymoshenko, who was jailed in 2011.
Klitschko told German newspaper Bild am Sonntag: "This was a poisoned offer by Yanukovich to divide our protest movement. We will keep on negotiating and continue to demand early elections. The protest by Ukrainians against the corrupt president must not have been in vain."
Opposition leaders say Yanukovich has betrayed Ukraine and are calling for a presidential election long before the next one is due in spring 2015. Klitschko said it must be held this year.
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The United States has warned Yanukovich that failure to ease the standoff could have "consequences" for its relationship with Ukraine. Germany, France and other Western governments have also urged him to talk to the opposition.
Russia on Saturday stepped up its warnings against international interference in Ukraine, telling European Union officials to prevent outside meddling and cautioning the United States against inflammatory statements.