Meanwhile, politicians who supported President Viktor Yushchenko during the 2004 Orange Revolution mass protests demanded he call new elections and vowed to rally their own supporters on Saturday.
The escalating tensions threatened to throw this country into political chaos once again, and exposed the difficulties that Yushchenko and Yanukovych have faced in governing jointly.
Yushchenko on Thursday accused the prime minister of violating the Constitution by poaching lawmakers from pro-presidential factions to expand his power base.
He challenged Yanukovych to join him in appealing to the Constitutional Court to uphold a law that prevents lawmakers from switching parties once in office.
Yanukovych did not respond publicly to the challenge, but said Friday that he talked with Yushchenko and the president was seeking a resolution to the crisis.
"It is a pity when small groups of politicians are unhappy that they aren't in power now and are trying at any price to hold early parliamentary elections, in violation of the Constitution," Yanukovych told about 5,000 supporters gathered on a Kyiv square.
Nearby, opposition leader Yulia Tymoshenko met with top members of Yushchenko's party and other figures.
Speaking to reporters, she warned that if he does not "he will lose what remains of the people's trust."
If Yushchenko "loves Ukraine and respects its people ... he will dissolve the parliament," Tymoshenko told reporters.
Vyacheslav Kyrylenko, who heads Yushchenko's faction in parliament, accused Yanukovych's Cabinet and coalition of usurping power and said opponents have "a recipe against it - to dissolve the parliament."
But Raisa Bohatiryova, head of Yanukovych's parliamentary faction, vowed to fight such a move. "We must defend the president from pressure and the effort to use him for unconstitutional activity," she said.
Yushchenko has been locked in an escalating battle for power with Yanukovych, with whom he faced off during the 2004 presidential campaign and the mass protests of the Orange Revolution.
Yanukovych's party put together a ruling coalition after winning the most votes in last year's parliamentary elections, and it has increasingly sidelined the president.
The simmering conflict burst into the open anew after numerous lawmakers from Yushchenko's party defected to join Yanukovych's parliamentary majority, giving it 260 votes in the 450-seat parliament.
Yanukovych's party has suggested it could soon reach 300 - enough to override presidential vetoes and make Yushchenko politically powerless.
"We want to see Yanukovych become president, he's the only one who is doing anything for Ukraine," said Sasha Pomanenko, 25, who carried a Yanukovych party flag.
The rally was full of university students; many said they had been paid to attend but refused to give their names.
Source: Kyiv Post