By Pavel Polityuk and Richard Balmforth
KIEV (Reuters) - Ukraine's opposition demanded a recount or a re-run in 13 constituencies on Monday, stepping up its campaign against the results of last month's parliamentary election which it says was rigged by President Viktor Yanukovich's ruling party.
Opposition leaders pressed their demands in talks on Monday night with election officials as 1,500 supporters remained outside the electoral commission's headquarters in Kiev to protest against alleged fraud in the October 28 vote.
After a day of tension, the commission said it was ready to stage a re-run in five of the disputed electoral districts, but that would require parliament's approval and might not completely defuse the situation.
Opposition leaders emerging from the talks welcomed the announcement which they said was better than allowing a Regions party victory. They said they would continue to campaign for a just result and encouraged their supporters to stay on the streets overnight.
"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 reporters at the commission's headquarters.
Prime Minister Mykola Azarov said on Friday the ruling Party of the Regions had nothing to do with the incidents at the center of the disputes, saying the overall results - which he said had handed victory to his party - were in line with exit-polls and pre-election surveys.
Even if the opposition was declared the winner in the disputed electoral districts the Regions would still keep its parliamentary majority as long as it had the support of its traditional communist allies and some independents.
However, a revision of the results could help galvanize anti-Yanukovich forces which have lost momentum since the jailing of Yulia Tymoshenko, one of the opposition's most prominent leaders and a former prime minister.
"WE ARE NOT ACCEPTING THE CHEATING"
The demand for a revision was signed by Tymoshenko's Batkivshchyna (Fatherland) party, Svoboda (Freedom) nationalists and the UDAR (Punch) party of boxing champion Vitaly Klitschko, and follows international criticism of the election in the former Soviet republic.
"We are not accepting the cheating that is going on," said Klitschko, who is WBC world heavyweight champion.
The numbers of protesters who have taken to the streets so far is much fewer than the tens of thousands who massed in Kiev in the winter of 2004-5 in what became known as the "Orange Revolution".
Those protests were also directed at an allegedly rigged election and doomed Yanukovich's first bid for the presidency, but he staged a comeback and beat Tymoshenko in a run-off vote for president in February 2010.
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 teargas 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 vote run-up, saying democracy had taken a "step backwards" since Yanukovich was elected in February 2010.
Assuming traditional support from its communist allies and independents, Yanukovich's Regions party is expected to have a working majority in the 450-seat parliament,
Yanukovich is likely to interpret an overall Regions victory as a mandate to continue policies which opponents say favor the big business industrialists who back him.
However, it is likely his leadership will 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 have criticized Yanukovich's leadership for corruption and cronyism, saying they will work together to defeat him when he seeks re-election in 2015.
On the streets of Kiev, opposition supporters said the integrity of the elections had to be protected.
"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 Andrew Osborn)