Opposition to end Ukraine blockade
 |  Yushchenko, left, and Yanukovych shake hands following Wednesday's news conference. |
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 |  VIDEO |
 Candidates in Ukraine's disputed presidential vote meet face-to-face.
 Opposition leader Viktor Yushchenko literally lost his face during the campaign.
 The continuing election dispute could hurt Ukraine's already fragile economy.
 A strong organization supports the thousands demonstrating in the streets of Kiev.
 How Russia's President Putin and the EU see the crisis.
 The U.S. has a significant stake in what is happening in Ukraine.
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KIEV, Ukraine (CNN) -- Prodded by international mediators, the two rivals in Ukraine's disputed presidential election met face-to-face Wednesday and reached a compromise agreement for the opposition to lift its blockade of government buildings and for both sides to work on unifying the country.
Ukrainian opposition leader Viktor Yushchenko sat down with his rival, Prime Minister Viktor Yanukovych, during a three-hour roundtable discussion that was mediated by outgoing President Leonid Kuchma and several European officials, including European Union foreign policy chief Javier Solana and the presidents of Poland and Lithuania.
"I would like to show you this document which is signed by all the participants of the roundtable without any exceptions," Kuchma said at a news conference announcing the agreement.
At the close of the news conference, the two rivals shook hands.
As part of the agreement, a working group had been formed to review Ukrainian law and to introduce appropriate proposals once the Supreme Court had reached its decision on the disputed election, Kuchma said.
The court has been meeting for three days and is expected to reach a decision this week.
Yushchenko appealed to the Supreme Court after the Central Election Commission declared Yanukovych -- backed by Kuchma in the presidential race -- the winner of the vote, despite widespread evidence of fraud documented by thousands of election observers.
"We all realize we will have to introduce amendments to the current legislation in the country," Kuchma said.
The parties are to meet again once the Supreme Court reaches its decision.
Wednesday's meeting got under way after a first round of discussions broke down. The international mediators worked to bring all sides back together.
Solana said he expected there would be more "ups and downs" in the days ahead, but he was optimistic a resolution would be reached.
"I am pretty sure we will solve the crisis in Ukraine," he told reporters.
Asked about the chances the Supreme Court might uphold the November 21 ballot, Solana said, "That's possible, but not likely. I don't think this will happen."
He would not discuss the date of a possible new election.
Solana said suggestions for an election within a month were probably too optimistic, although he believed it should be held as soon as possible.
He also said he believes the two candidates should be allowed to participate in any possible new election -- whether it be a run-off or entirely new election.
International monitors and Western governments, including the United States, have refused to recognize the results of the run-off.
But Russian President Vladimir Putin has twice telephoned his congratulations to Yanukovych and has told Western leaders that Ukraine must settle the dispute without their interference.
Wednesday's roundtable discussion came after a whirlwind day in which the Ukrainian Parliament voted to fire the government of Yanukovych -- a no-confidence vote that narrowly passed with 229 votes, just three above the 226 plurality.
Thousands of Yushchenko supporters outside the building erupted in cheers upon the news.
But Yanukovych immediately dug in his heels. "I will never recognize this decision," he said. "They approved the decision in political terms. But it is against the law, it is against the Constitution."
The no-confidence vote now goes to Kuchma, who can allow the current government to continue for up to 60 days until a new Cabinet is formed.
Hundreds of thousands of Yushchenko supporters have camped in tents and rallied in snow-covered Independence Square and the streets around it since the November ballot.
At times, they have blocked government buildings and hampered some government operations, but the protests have all been non-violent.
Under Wednesday's agreement, Yushchenko said the blockades of government buildings would stop.
Yushchenko's support comes mainly from Ukraine's west, where closer ties with Europe are supported, while Yanukovych is strongly backed in the mainly Russian-speaking, industrialized east, bordering Russia.
The governing councils of three eastern regions initially said they would allow non-binding referendums on creating a separate, autonomous region in a newly created Ukrainian federation, but they have backed away from those threats after talks with Kuchma.
Representatives of both sides in the dispute have said they do not want to see the country split.
CNN's Jill Dougherty, Max Tkachenko and Ryan Chilcote contributed to this report.