Ukrainian opposition leader Viktor Yushchenko has appealed to the police and the army to join the protests over the disputed presidential election.
Viktor Yushchenko has called for a campaign of civil disobedience
The call followed a stormy session of parliament in which Mr Yushchenko took a symbolic oath of office in front of his supporters.
He also urged more than 200,000 people gathered in central Kiev to continue their demonstrations.
Official results showed a narrow win for Prime Minister Viktor Yanukovych.
Exit polls had indicated a clear win for Mr Yushchenko, who has refused to accept the official result and is calling on protesters to mass in Kiev's Independence Square.
There are reports of protesters marching from the square to the offices of Leonid Kuchma, the outgoing president. He has called for a peaceful solution.
Jailed twice in his youth
Former governor of industrial Donetsk region
Raised pensions and public sector pay before election
Would make Russian second official language and allow dual citizenship
Was prime minister 1999-2001
Has an American wife
Promises to fight corruption, create five million jobs and pursue free market reforms
Would seek deeper relations with the West
The security forces warned earlier that they are ready to put down any lawlessness "quickly and firmly".
Mr Yanukovych has criticised the call for public protests and said a "small group of radicals" was trying to split the country.
The parliamentary session had been called to discuss the dismissal of the electoral commission, but no vote was taken because pro-government deputies boycotted the session.
The session was suspended and live television coverage was cut off just before Mr Yushchenko recited an oath of office.
The move has no legitimacy, but Mr Yushchenko put his hand on a Bible and swore to "defend the rights and liberties of Ukrainian citizens", as the crowd listened on loud speakers outside.
Moscow appeals for calm
Following the parliamentary session, police locked all the windows and doors, briefly trapping dozens of MPs, journalists and diplomats inside.
The authorities feared the protesters may try to storm the building after some people broke through the security cordon.
International observers have described Sunday's poll - a second round run-off - as seriously flawed, and the US and European Union are calling for an urgent review.
Russian President Vladimir Putin, who backs Mr Yanukovych, appealed for a non-violent solution to the dispute.
Moscow congratulated Mr Yanukovych on Monday, but Mr Putin has now said that he could not accept or deny the results because they had still not been officially announced.
In a statement earlier on Tuesday, Mr Yushchenko said he had won a "convincing" victory and called on nations to recognise him as the winner.
The statement said the opposition would continue "a campaign of civil disobedience" and "a non-violent struggle for recognition of the true results of the election".
Mr Yushchenko has called on the former Polish president and leader of the Solidarity trade union Lech Walesa to mediate in the crisis, and he has accepted.
Mr Walesa said he was ready to travel immediately to Ukraine - as long as President Kuchma agrees.
It was the second day of mass rallies in support of Mr Yushchenko - despite freezing cold.
The opposition says it has recorded many thousands of irregularities in the election, including very high turnouts in government strongholds.
Protesters gathered in huge numbers despite the cold
Pro-Yushchenko demonstrations have also taken place in western Ukraine, where a number of municipal councils have joined Kiev council in refusing to accept the outcome of the election.
By contrast, in the pro-Russian east of the country, where the government has most of its support, there have been protests at which the opposition leader was accused of unleashing extremism
The central electoral commission proclaimed Mr Yanukovych the winner, with 49.4% to Mr Yushchenko's 46.7%.