But the political crisis that has paralysed this country for the past nine days showed signs of easing as opposition protesters lifted their blockade of government buildings in the capital.
A key Russian-speaking region has also put plans on hold to back away from the rest of the country.
The supreme court, meanwhile, held a second day of closed-door deliberations on claims from Viktor Yushchenko, the Western-oriented rival presidential contender, that the 21 November elections were blatantly rigged by the authorities and should be annulled.
Soon after parliament went into session, Yanukovich indicated he was interested in finding a negotiated way out of the crisis, saying that if the victory officially handed to him by the election commission were upheld, he would offer the post of prime minister to Yushchenko.
Yanukovich also stated that if the supreme court ruled that the election was indeed too flawed for the results to stand, then new elections should be held - but with the caveat that neither he nor Yushchenko be allowed to stand in them.
If the ballot is cancelled, "I will propose organising a new election in Ukraine with the participation of neither me or Viktor Yushchenko", Yanukovich said.
There was no immediate response to Yanukovich's proposals from the Yushchenko camp, but it was far from certain that either of the offers would be accepted as Yushchenko supporters say their man in fact won the vote and is the country's legitimate new leader.
Yushchenko supporters say he won
the vote and should be president
After more than a week of a high-tension stand-off between the rival camps that at times seemed to push this nation of 48 million to the brink of civil conflict and division, outgoing President Leonid Kuchma broke the deadlock on Monday with a call for repeat elections.
Several thousand Yushchenko supporters gathered outside the parliament offered little indication they were prepared to accept anything short of seeing their man installed as the next Ukrainian president.
"We want this government out," said Ihor Hrivnak, from the western Ivano-Frankivsk region. "Kuchma won't have a choice but to fire Yanukovich."
Slava, a 29-year-old sociologist, said: "I don't think there will be a revote. Yushchenko will be declared the winner. What's the point of spending more money on holding a new election? Everybody knows he won."
Meanwhile, the parliament in Ukraine's Russian-speaking eastern Donetsk region postponed its emergency session to discuss a planned referendum on more autonomy as the governor urgently rushed to Kiev for meetings, a spokeswoman said.
Parliament is debating a vote of
no confidence in Yanukovich
"The issue [of the referendum] is hanging in the air," said Olena Bondarenko, spokeswoman for the regional administration.
The national parliament meanwhile, debated a non-binding measure of no-confidence in Yanukovich put forward by the Yushchenko camp.
Although such a resolution, if approved, would have no legal effect, it would nonetheless mark an important symbolic victory for Yushchenko and a popular reprimand of Yanukovich.
Split or bloodshed
The speaker of parliament in neighbouring Russia, meanwhile, warned that Ukraine was heading either for a split or for bloodshed, and blamed opposition protesters for failing to keep a promise to clear the streets.
"What is happening in Ukraine saddens us," said Duma Speaker Boris Gryzlov in Moscow. "The situation is heading towards a split or towards bloodshed."
Yanukovich, who favours continuing close ties with neighbouring Russia, was Kuchma's preferred successor, and also had tacit but potent support from Moscow.
His strongest support lies in the mainly Russian-speaking eastern half of Ukraine.
Yushchenko, himself a former prime minister under Kuchma, has by contrast said he would focus more on developing stronger relations with the West.
His base of support lies mainly in the Ukrainian-speaking west of the country and among younger people.