U.S. officials urged Russia to join with the United States in helping the former Soviet republic. "Let's all join together now and see what we can do," Secretary of State Colin Powell said.
Setting aside the vigorous backing Russian President Vladimir Putin gave Yanukovych in his campaign for the presidency, Powell said, "I don't expect this to be a blot on U.S-Russian relations."
The pro-Western candidate, Viktor Yushchenko, appeared to be the winner of a runoff Sunday after Ukraine's Supreme Court threw out an earlier runoff Yanukovych victory amid U.S. and European allegations of widespread corruption.
While "some shortcomings remain," Powell said, "it appears that the Ukrainian people finally had an opportunity to choose freely their next president."
Yanukovych refused Monday to concede defeat in Ukraine's weekend presidential election, and said he would go to the Supreme Court to challenge the results.
"I will never recognize such a defeat, because the constitution and human rights were violated in our country and people died," Yanukovych told reporters in the capital Kiev.
Official results from Sunday's vote, with ballots counted from 99.66 percent of precincts, gave opposition leader Viktor Yushchenko 52.09 percent compared to Yanukovych's 44.12 percent. Turnout was 77.2 percent.
Many Ukrainians appeared to be celebrating Yushchenko's victory Monday.
"It's almost like a street carnival kind of an atmosphere that's taken over the whole center of Kiev, and even though it's a Monday night, the street is absolutely packed," reports CBS News' Bill Gasperini.
Rejecting any suggestion the Bush administration backed Yushchenko, Powell said U.S.-funded organizations such as the National Endowment for Democracy merely helped Ukrainian citizens to participate in open, free elections.
"All we wanted to see was a full, free, fair election, and that appears now to be what happened," he said.
But Dimitri Simes, president of The Nixon Center, said there was much more to it than that.
"We were not just training observers and not just providing education to Ukrainian judges," Simes said. "We were helping people in civil disobedience."
But analysts had seen a victory by the pro-Western leader of the Orange revolution an opportunity for Ukraine to align itself more directly with European groupings.
Yanukovych, by contrast, was seen as looking eastward toward Russia.
"I am delighted," said Radek Sikorski, director of the new Atlantic Initiative at the American Enterprise Institute. "A reformer and friend of the West and someone as levelheaded as Yushchenko has won and won convincingly."
Sikorksi, a former deputy foreign minister of Poland, said the United States should signal Yushchenko that "if Ukraine wants to join the club of the democratic West it will be welcome."
At the same time, Sikorksi in an interview urged Russia to "revise its attitude" toward former Soviet republics that "it patronizingly calls the Near Abroad."
"Russia has to get used to the fact that Ukraine is an independent country," he said.
Simes said that from the Western standpoint, Yushchenko was a better candidate, adding, "We should be pleased when he is certified the winner."
"We should help him with Ukraine's involvement in international institutions," Simes said. "But we should not promise more than we can provide and not encourage him to have an artificial conflict with Russia."
Bruce George, head of the delegation from the Organization for Security and Cooperation in Europe, Parliamentary Assembly of the Council of Europe and other election watchdogs said the third round of voting showed progress in many areas of former concern.
"There was no gross abuse of administrative resources. The campaign conditions were more equal. There was less difference in media coverage. Our observers reported less pressure on voters. The election administration was more transparent and fairer," he said.
Another Canadian observer, lawmaker David Kilgour, said election officials in the eastern region of Luhansk "worked in difficult conditions."
"We walked with them through knee-deep mud to bring mobile ballot boxes to old ladies who could hardly sign the ballot, but were so eager to vote," he said.
Also Monday, Ukrainian Transport Minister Heorhiy Kirpa was found dead with a gunshot wound, a spokesman for the nation's railways said.
The death came a day after presidential elections in which Prime Minister Viktor Yanukovych, whom Kirpa strongly supported, trailed opposition leader Viktor Yushchenko. Opposition figures had claimed Kirpa allocated trains to ferry Yanukovych supporters to vote at multiple polling stations in presidential balloting last month that was annulled by the Supreme Court.
Kirpa's body was found in his country house just outside the Ukrainian capital Kiev, spokesman Eduard Zanyuk said.
"The man has passed away. An investigation will clear up the circumstances," Zanyuk told The Associated Press.
Local media speculated that the death was a suicide, but officials did not confirm that. The Unian news agency reported that a gun was found near the body.