Liberal opposition challenger Mr Viktor Yushchenko said a solution to Ukraine's political crisis was needed within days and insisted on a new vote to make up for a presidential election he alleged was tainted by fraud.
Mr Yushchenko, addressing tens of thousands of supporters in Kiev's Independence Square, said he had rejected a proposal by Prime Minister Viktor Yanukovich, declared the winner of the poll, to submit irregularities to the courts.
"The prime minister cannot hear you. He is offering things which drive Ukraine further from a solution to this political crisis," he said. "We will only hold talks on staging a new vote," he said.
Earlier the candidates in the presidential election and mediators said today they had set up a working group for further talks, but reached no other agreement on resolving the crisis.
Outgoing Ukrainian President Mr Leonid Kuchma said Mr Yanukovich and Mr Yushchenko had agreed to set the working group in motion immediately. Both sides agreed to renounce violence.
The contenders sat down with European and Russian mediators to try to end a crisis over a disputed election that has led to mass street protests and pushed the country toward civil conflict.
"It is our hope that if all participants show the desire and the will, a compromise will clearly be found," Mr Kuchma told the meeting in the presidential Mariinsky Palace.
The meeting, involving one of Europe's top trouble-shooters and a trusted lieutenant of Russian President Mr Vladimir Putin, reflected the high level stakes for East and West in the future of ex-Soviet Ukraine.
It followed a fifth straight day of mass street protests in the capital Kiev by supporters of Mr Yushchenko who says the victory of Prime Minister Mr Yanukovich in a Sunday election was rigged.
Supporters of Mr Yushchenko, who says he was the real winner, blocked official buildings and challenged the government's control of the country.
Mr Yanukovich hit back at Mr Yushchenko appealing to his followers to avert an "unconstitutional coup".
"Dear friends, together we must do everything so that an unconstitutional coup in Ukraine does not happen," Mr Yanukovich told thousands of his own supporters chanting his name.
Most were young men brought to Kiev by train from the Donbass coalfield in his power base - the Russian-speaking east of the country.
Mr Yanukovich referred to Mr Yushchenko as a "pesky cat" - the name of a Soviet-era cartoon character - saying he challenged his rival to show up at the talks.
Apart from the two rivals and Mr Kuchma, the other participants were European Union foreign policy chief Mr Javier Solana, Polish President Mr Aleksander Kwasniewski and Russian parliament speaker Mr Boris Gryzlov.
A spokeswoman for Mr Solana, said of the meeting with the two candidates: "The intention is to signal the beginning of a political dialogue."
President George W. Bush said today he hoped the crisis over the Ukrainian elections will be resolved and said the international community was watching closely.
"There's a lot of allegations of vote fraud that has placed their elections ... in doubt," Mr Bush told reporters during an outing on his Thanksgiving vacation at his Texas ranch.