By Pavel Polityuk and Richard Balmforth

KIEV (Reuters) - Ukraine's opposition demanded a recount or a fresh vote in a dozen hotly contested constituencies on Monday, stepping up their campaign against a parliamentary election last month they say was rigged by President Viktor Yanukovich's ruling party.

Hundreds of people gathered outside the Central Electoral Commission headquarters in the capital Kiev to protest against fraud in the October 28 vote, defying warnings by police that the protest was illegal and might be broken up by force.

An opposition victory in the disputed electoral districts would still leave the president's Party of the Regions with a parliamentary majority, but could help galvanize anti-Yanukovich forces that have lost momentum since the jailing of their leader, ex-Prime Minister Yulia Tymoshenko.

"We are demanding that the Central Electoral Commission announce the result of voting in 13 districts where, according to the final tally, the opposition won," Arseny Yatsenyuk, leader of the united opposition said.

"In those cases where it is impossible to establish the result a re-run should be announced," he told journalists at commission headquarters in Kiev where the rally was staged.

The demand for action was signed by Tymoshenko's Batkivshchyna (Fatherland) party, Svoboda (Freedom) nationalists and the UDAR (Punch) party of heavyweight boxing champion Vitaly Klitschko, and follows international criticism of the election in the former Soviet republic.

Prime Minister Mykola Azarov on Friday said the Regions had nothing to do with the disputes at the centre of the latest protests, and said the overall results were in line with exit-polls and pre-election surveys.

Anger erupted in several electoral districts at the weekend, with election officials conducting the vote-count besieged by opposition supporters and members of the Regions party. Riot police used tear gas to quell trouble in one district.

Observers from Europe's OSCE rights and security body criticized misuse of state money and resources and biased media coverage in the run-up, saying democracy had taken a "step backwards" since Yanukovich was elected in February 2010.

A 500-member team from Canada said their observers had often been excluded from counting rooms and reported evidence of attempts to manipulate results.

In a statement on Saturday, EU foreign policy chief Catherine Ashton and EU Commissioner for Enlargement Stefan Fule urged authorities and parties "to finalize the tabulation allowing for the rapid announcement of the final results, which should reflect the genuine will of the Ukrainian voters."

REGIONS MAJORITY

Whatever the outcome in the 13 contested areas, Yanukovich's Regions party is expected to have a working majority in the 450-seat parliament, assuming traditional support from its communist allies and independents.

An overall Regions victory is likely to be taken by him as a mandate to continue policies which opponents say favor the big business industrialists who back him.

However, his leadership will likely continue to be cold-shouldered by the United States and the European Union over the imprisonment of Tymoshenko. The EU has already refused to settle a major free trade pact because of her case.

Opposition leaders Yatsenyuk, Svoboda's Oleh Tyahnybok and the two-meter-tall Klitschko - said they were prepared to refuse to recognize the election and boycott parliament if their demands were not met.

They criticize Yanukovich's leadership for corruption and cronyism and say they will work together to defeat him when he seeks election in 2015.

On the streets of Kiev, opposition supporters said the integrity of elections had to be protected.

"We are protesting. We want to defend our votes. The Party of the Regions has falsified the elections, taken our victory. It is us who ought to have the majority not them," said 50-year-old Nadezhda Storozhuk, a Batkivshchyna supporter.

"We have turned out to defend the interests of simple people who have voted and whose votes have been stolen. We are ready for other kinds of action if need be," said Yuri Derkach, 45, a supporter of Svoboda.

(Writing by Richard Balmforth and Olzhas Auyezov; Editing by Jon Boyle)