"We cannot accept this result as legitimate because it does not meet international standards and because there has not been an investigation of the numerous and credible reports of fraud and abuse," Powell said.
He added that a failure to investigate the alleged fraud would lead to unspecified "consequences" in bilateral ties.
Powell twice eluded questions about the open support that Russian President Vladimir Putin has lent Ukrainian President Leonid Kuchma and his heir-apparent, Yanukovych, before and after the vote.
Yet it is likely that Powell's message was indirectly addressed to Moscow.
Reports say the State Department this week called in the Russian ambassador to the United States and expressed concern at Putin's early embrace of Yanukovych.
The Russian president on 22 November prematurely congratulated Yanukovych on his election. He subsequently backtracked as Ukraine's Central Election Commission later said it was withholding the final outcome of the vote.
Viktor Kremenyuk is deputy director of the USA and Canada Institute at Russia's Academy of Sciences. He told RFE/RL that Moscow's insistence at supporting the outgoing Kuchma administration might affect relations with Washington -- at least on the diplomatic level.
"Of course there will be consequences," Kremenyuk said. "To a great extent, these consequences will depend on the stance Moscow will adopt in the coming days. The ball is in our camp now. The Americans have made their position perfectly clear and explained why they do not recognize the outcome of the elections. Now it is up to Moscow to make its reaction public."
The European Union and the European Parliament today added their voices to that of the United States to demand that complaints of election fraud be investigated.
EU leaders were expected to press Putin to clarify his position today at a previously scheduled EU-Russia summit in The Hague.
Yet just hours before that summit started, Putin's office issued a statement congratulating Yanukovych once again on his election. The statement said the vote showed the Ukrainian people had opted "for stability and the strengthening of statehood."
Putin welcomed Yanukovych's election as an opportunity to develop further the "strategic partnership" that exists between Russia and Ukraine.
Kremenyuk said that with regard to Russian-U.S. ties, much will depend on Moscow's further steps.
"Should [Moscow] eventually decide to behave normally and say that, indeed, there is a need for a thorough investigation [into the elections], then Russia and the United States might well work together so that order is restored as quickly as possible in Ukraine," Kremenyuk said. "Should it, on the contrary, persist in its opposition and pride, should it continue to say that it knows everything about the situation in Ukraine and that it does not need any additional information, then conflicts [with U.S. interests] would likely arise."
Vladimir Pechatnov chairs the European and American Studies department at Moscow State Institute of International Relations (MGIMO). He said that, in his opinion, U.S.-Russian relations are going through a crucial stage.
"With respect to the overall effect the [Ukrainian] crisis may have on our relations [with the U.S.], I would say that it certainly complicates them. Both our countries are undergoing a serious test that will show whether they can find a common understanding and restrain each other with respect to Ukraine," Pechatnov said. "[This country] is much important to us than it is for the U.S., but I don't think Russia wants at all costs that such and such candidate wins this election. It is in Russia's interest that the situation does not get out of control and that everything remains within the framework of the Ukrainian laws and constitution. Of course it is inevitable that the U.S. holds Russia responsible for further developments in Ukraine. But one could equally raise the issue of the U.S. responsibility in the present situation."
Pechatnov said it is essential that Moscow and Washington put their differences aside and join forces to help rival sides in Ukraine settle their dispute.
"If that does not happen, then the chances will be higher that the situation in Ukraine gets out of control," Pechatnov said. "Only concerted steps aimed at reconciling both sides and involving the U.S., Europe, and Russia may help defuse this dangerous situation and facilitate a [peaceful] outcome. I believe that we should all seek a solution instead of issuing ultimatum-like statements."
Many say neither Moscow nor Washington -- which have been engaged in active cooperation in both the energy and security fields, including in Central Asia and the Caucasus -- has an interest in putting their relations at risk for the sake of Ukraine.
Pechatnov said that is especially true since it remains to be seen whether the West-leaning Yushchenko would really conduct a fully pro-Western policy once in office -- or conversely whether Yanukovych would pursue a selective relationship with Russia if he were to be sworn in.
Pechatnov said it is one thing to make campaign pledges and another thing to deal with political reality.