Thousands of opposition supporters have been demonstrating outside Ukrainian government offices in a second night of protests over presidential elections.
The two days of protests have so far remained peaceful
Tens of thousands more rallied nearby in Kiev's Independence Square to protest against the official victory for Prime Minister Viktor Yanukovych.
The rallies were peaceful, and most protesters went home for the night.
Opposition leaders said they had accepted an offer of talks from outgoing President Leonid Kuchma.
Viktor Yushchenko, the opposition challenger who says the vote was rigged against him, earlier appealed for police support.
"Ukraine needs you, come over to our side," he urged police and civil servants.
But Mr Kuchma interrupted a televised football match with a defiant statement attacking the opposition's actions.
Jailed twice in his youth
Raised pensions and public sector pay before election
Would make Russian second official language and allow dual citizenship
Was prime minister 1999-2001
Promises to fight corruption, create five million jobs and pursue free market reforms
Would seek deeper relations with the West
"This political farce being played out now [by the opposition]... is very dangerous and can lead to unforeseen consequences," Mr Kuchma said in a message read out by a presenter.
He said authorities would not be the first to use force but were "ready to uphold law and order".
A hardcore of opposition supporters are still gathered outside the presidential building but most have now gone home for the night.
Down the road, in Independence Square, thousands have been maintaining a night-time vigil.
Official results from Sunday's run-off election showed a narrow win for Mr Yanukovych, although exit polls had indicated a clear win for the pro-Western opposition leader, himself a former prime minister.
Mr Yanukovych, who has the backing of Russia, has said a "small group of radicals" are trying to split the country.
Earlier, in a stormy session of parliament, Mr Yushchenko put his hand on a Bible and took a symbolic oath of office in front of party supporters, as 200,000 people listened to events relayed outside by loudspeakers.
The session was suspended and live television coverage was cut off just before Mr Yushchenko spoke.
The opposition says it has recorded thousands of voting irregularities, including very high turnouts in government strongholds. International observers have described the poll as seriously flawed.
On Tuesday two members of the central election commission urged their 13
colleagues not to certify the final election results, which gave Mr Yanukovych 49.4% of the vote to Mr Yushchenko's 46.7%.
In other developments:
- Pro-Yushchenko demonstrations also take place in western Ukraine, where a number of municipal councils have joined Kiev council in refusing to accept the outcome of the election
- In the east of the country, where the government has most of its support, there are demonstrations accusing the opposition leader of unleashing extremism
- Also in the east, tens of thousands of opposition supporters demonstrate in Ukraine's second city, Kharkiv
- Mr Yushchenko calls on the former Polish president and leader of the Solidarity trade union Lech Walesa to mediate in the crisis. Mr Walesa says he is ready to travel immediately to Ukraine - as long as President Kuchma agrees.
A White House spokeswoman earlier called for Ukrainian authorities not to certify the election until the fraud allegations are investigated.
UK Foreign Minister Jack Straw echoed the call, saying: "The Ukrainian authorities should investigate all allegations of fraud to ensure that the result reflects the democratic will of the Ukrainian people."
Meanwhile, a day after congratulating Mr Yanukovych on his win, Russian President Vladimir Putin said that he could not accept or reject the results because they had still not been officially announced.
State television has not shown pictures of the events in Kiev and dozens of journalists have resigned over what they say is state censorship.