Yushchenko declared victory early yesterday after election officials suggested he had an unassailable lead in the vote count.
Preliminary figures late last night showed Yushchenko with 52 percent versus Yanukovych's 44.2 percent, with ballots counted from 99.89 percent of precincts, AP reported. The Central Electoral Commission announced that turnout was over 77 percent.
"I will never recognize this defeat because there were violations of the constitution and of human rights in our country," Yanukovych said last night.
Candidates have seven days to appeal once the country's Central Election Commission issues its final preliminary tally.
Yanukovych stressed that he has not urged his supporters to mount public demonstrations, AP reported.
The Yanukovych campaign team has collected almost 5,000 complaints so far concerning the fairness of the balloting, the prime minister told reporters.
He criticized election-law reforms passed between the abortive runoff and the 26 December vote that restricted home voting, which was blamed for some of the fraud that marred the November vote. That restriction was nullified by the Constitutional Court on the eve of the ballot.
Polish President Aleksander Kwasniewski has already congratulated the opposition leader on his victory, according to a press release from Kwasniewski's office quoted by Reuters.
The Organization for Security and Cooperation in Europe (OSCE) took a different view, saying yesterday that the vote shows the country had taken "a great step forward toward free and fair elections."
The head of the OSCE observer mission, Bruce George, said this was the general view among the monitoring organizations.
"I am much happier to be in a position to announce that it is the collective judgment of these organizations represented here that the Ukrainian elections have moved substantially closer to meeting OSCE and other European and international standards," George said.
However, George added that the election was not perfect and that the mission's final report will detail what observers saw as its shortcomings.
The repeat vote was monitored by some 12,000 international observers.
European Union High Representative for Common Foreign and Security Policy Javier Solana called on Ukraine's political leaders to work together to unite the country after the divisive election.
U.S. Secretary of State Colin Powell broke the official silence in Washington today over the vote and called the Ukrainian election "a historic moment for democracy." He said it appeared the Ukrainian people had had the opportunity to choose their own government and added the election appeared to have been "full and free."
In the early hours yesterday, after three separate exit polls showed he had a big lead, Yushchenko went to Independence Square in the heart of the capital to address his supporters.
They welcomed him with the same chants of "Yushchenko" that have echoed around the capital and the country for the past month in a nonstop protest against the government. It was in that same square that hundreds of thousands of Yushchenko supporters gathered on the evening of 21 November to protest the massive fraud perpetrated by the government in that day's first presidential runoff.
Yushchenko predicted that the opposition would emerge with a win.
"Dear friends, I would just like to say, for 14 years we were independent, but we weren't free," Yushchenko told the crowd. "For 14 years there was tyranny in all of Ukraine, the tyranny of [outgoing President Leonid] Kuchma, [his predecessor Leonid] Kravchuk, and [Prime Minister] Yanukovych. Today we can say that is all in the past; before us lies an independent and free Ukraine."
"Today we are turning the page of disrespect for people, of lies, censorship, and violence," Yushchenko said. "The people who were dragging Ukraine into a hole are at this moment becoming [a part of] the past. A new epoch is beginning of a new great democracy. Many tens of millions of Ukrainians have dreamed of this."
The flawed vote sparked 17 days of demonstrations that have since become known as the "Orange Revolution" -- for the orange color the Yushchenko campaign adopted.
Yushchenko, flanked by his wife and senior political allies, bowed yesterday to supporters and said: "My first thanks are to you. The people proved their power. They rebelled against probably the most cynical regime in Eastern Europe."
Yushchenko has said his ambition is for Ukraine to join NATO, the European Union, and the World Trade Organization (WTO). He has said that he will cooperate with Moscow as an equal but added that the era during which Ukraine was treated as a subordinate was over.
Russia's President Vladimir Putin had openly backed Yanukovych, arriving in Ukraine on the eve of two earlier rounds of elections, in October and November, to boost Yanukovych's chances. Putin was quick to congratulate Yanukovych for his official victory on 21 November, a win marred by sufficient fraud to prompt the Supreme Court to order the new vote.
Yanukovych supported Putin's plan to re-create a Moscow-led bloc, comprising Ukraine, Belarus, Kazakhstan, and Russia. That scheme now looks doomed.
Yanukovych courted Ukraine's large ethnic-Russian minority -- around 9 million of the country's 48 million population -- with promises that Russian would become a state language.
Russia's interference had caused resentment among opposition supporters. Many of Yushchenko's close colleagues suspect Russia of involvement in the nearly fatal poisoning of the opposition leader in September that has left his face badly disfigured. The EU and the United States rebuked Putin for meddling in the election.
But the results from yesterday's vote suggest once more that Ukraine is deeply divided, with the western and central regions backing Yushchenko while the east mostly supported Yanukovych.
Yanukovych's senior political allies in some of the eastern regions threatened in November to seek autonomy, something they have since moved away from. A member of parliament from the Social Democrat Party-united, which supported Yanukovych, Ihor Shurma, suggested some kind of devolution might happen -- but not for a while.
"Perhaps a federal model will be beneficial for Ukraine, but not today. Ukraine is not ready for that today," Shurma said. "Economically it's not strong enough. At present it faces many risks. Therefore, it is not appropriate to raise this question at this time."
In an early hint that he might accept the results of yesterday's vote, Yanukovych promised to form a robust opposition in parliament to any Yushchenko-appointed government.
The leader of his campaign team, Taras Chornovyl, even predicted Yanukovych supporters in parliament would attract some of Yushchenko's current political allies, including the Socialists and the Yuliya Tymoshenko Bloc, to fight the parliamentary elections scheduled for 2006 as a coalition.
"If Yushchenko indeed does become president, then I think that in the near future politicians like Yuliya Tymoshenko and others will join us," Chornovyl said.
(RFE/RL and wire reports)
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[For more RFE/RL coverage and analysis, see our dedicated "Ukraine's Disputed Election" website.]