Updated

Outgoing President Leonid Kuchma (search) called for negotiations in Ukraine's spiraling political crisis Tuesday, hours after the leader of the opposition declared himself the winner of a disputed presidential election to the approval of tens of thousands of protesters.

Another top opposition figure accepted Kuchma's proposal even though she had declared earlier on a third day of high tensions that negotiations were unthinkable.

"We now have decided to give the possibility to Kuchma to form proposals for talks," Yuliya Tymoshenko said, according to the Interfax news agency. It was not immediately clear when talks might take place.

The proposal for negotiations between the candidates — Kuchma-supported Prime Minister Viktor Yanukovych (search) and the Western-leaning reformer Viktor Yushchenko (search) — was out of character for the president, who is not known for compromising. But neither side held a clear advantage, and both had much to lose if violence should break out.

Earlier in the day, Yushchenko threatened a campaign of civil disobedience to back the opposition's charge that authorities rigged Sunday's vote in favor of Yanukovych.

"Ukraine is on the threshold of a civil conflict," Yushchenko told lawmakers gathered for an emergency session. "We have two choices: Either the answer will be given by the parliament, or the streets will give an answer."

The Bush administration urged the Ukrainian government not to certify results from Sunday's runoff election that showed Yanukovych edging Yushchenko.

"The United States is deeply concerned by extensive and credible indications of fraud committed in the Ukrainian presidential election," White House spokeswoman Claire Buchan said.

But Russian President Vladimir Putin, who supported Yanukovych in the campaign, criticized Western assessments of the vote as flawed, stressing that the results were not yet official. On a state visit to Portugal, he called for calm and respect for the law in this former Soviet republic.

As snow fell Tuesday night, more than 10,000 Yushchenko supporters marched to the presidential administration building, skirting some heavy trucks that blocked the street and facing off with hundreds of police in riot gear guarding the building.

Police estimated the total number of demonstrators in the streets Tuesday at 40,000 but independent estimates ranged as high as 200,000.

After a few hours, many demonstrators headed home, while some went back to a tent city set up on Kiev's main avenue and Independence Square, where they pledged to stay until Yushchenko is declared president. A core group remained outside the administration building, apparently as part of a deal worked out in negotiations between Tymoshenko and security forces.

Yanukovych supporters early Wednesday were building their own encampment at a stadium several blocks from the opposition site. The proximity of opposing sides raised new prospects of confrontation.

Kuchma's statement, which was read on state television, referred to the demonstrations as a "political farce" that is "extremely dangerous and may lead to unforeseeable consequences."

Although the harsh description seemed to indicate Kuchma was not inclined to take the opposition's position seriously, he nonetheless called for all political factions to enter into talks.

"We should peacefully and with consideration discuss the complicated situation and propose to society real steps for getting out of the crisis," the statement said.

"I am convinced today that this is the only route in the search for a balanced position on not allowing Ukraine to split into pieces," it added.

The election commission's announcement that Yanukovych led Yushchenko galvanized anger among many of Ukraine's 48 million people. Official results, with more than 99.48 percent of precincts counted, put Yanukovych ahead with 49.39 percent of the votes to his challenger's 46.71 percent. But several exit polls indicated Yushchenko was the winner.

Western observers criticized the election as widely flawed by multiple voting and apparently inflated turnout figures in Yanukovych's stronghold eastern districts.

In Washington, four diplomats at Ukraine's embassy signed a declaration accusing their government of subverting the will of the people by favoring Yanukovych.

"We cannot quietly look away as Ukraine's future is buried along with the future of our children," read the statement, signed by counselor Oleksandr V. Shcherba, Second Secretary Yuriy B. Parkhomenko, counselor Oleksandr V. Potiekhin and counselor Volodymyr M. Chumak.

Russia, meanwhile, lashed out at the United States for what it called "unprecedented interference" in domestic affairs after U.S. officials allegedly took Moscow to task for recognizing Yanukovych's victory.

Demonstrations have been peaceful so far, but fears ran high they could deteriorate into violence — either out of the protesters' frustration or attacks by Yanukovych supporters.

Tens of thousands of Yushchenko supporters cheered their candidate outside parliament during the special session Tuesday, waving orange flags and chanting "Criminals go away!" With many of the prime minister's backers absent, the session did not muster a quorum and concluded without taking action on a measure to nullify the election.

Immediately afterward, Yushchenko went to the podium and took an oath of office, his right hand on the constitution and his left on a Bible. Pro-Yushchenko lawmakers, who had urged him to take the oath, shouted, "Bravo, Mr. President!"

The irregular procedure was not legally binding, parliament speaker Volodymyr Lytvyn said. But its symbolic weight was considerable — a declaration that Yushchenko did not intend to back off.

A half-dozen large cities already have declared they recognize Yushchenko as president, and Kiev's city council called on the national parliament to declare the vote invalid.

In televised comments, Yanukovych called for national unity, saying: "I categorically will not accept the actions of certain politicians who are now calling people to the barricades. This small group of radicals has taken upon itself the goal of splitting Ukraine."