US Secretary of State Colin Powell has dismissed suggestions from Russia that Washington and its allies are trying to extend their influence into Ukraine.
Mr Yushchenko (left) says last month's poll was rigged against him
He spoke as a European security meeting ended without a full endorsement of plans to re-run Ukraine's election.
Mr Powell said the people of Ukraine deserved fair elections - and did not have to choose between East and West.
On Monday, Russia's President Vladimir Putin warned against Western expansion into former Soviet countries.
The government and opposition in Kiev have failed to reach a comprehensive deal, despite six hours of talks that ended in the early hours of Tuesday.
But the two sides did agree to appoint a new central election commission, and on the need for electoral reform before the re-run of the presidential poll.
The talks, attended by the country's outgoing President Leonid Kuchma, were mediated by foreign observers including the European Union's foreign policy chief, Javier Solana.
The sticking points are the question of constitutional reforms and opposition demands to sack the government.
Parliament in Kiev has been debating the reforms, which would reduce the powers of the new president.
The second round of the disputed election is due to be re-run on 26 December between the opposition leader, Viktor Yushchenko, and Prime Minister Viktor Yanukovych.
Mr Yanukovych was declared the winner of last month's poll but the opposition - backed by foreign observers - alleged massive fraud. The re-run was ordered by the Supreme Court on Friday.
Washington has also backed the court decision, but a low-key closing statement in Sofia reflected disagreements between foreign ministers at the meeting of the Organisation for Security and Co-operation in Europe (OSCE).
Reading a closing statement on behalf of "most" - but not all - OSCE members, Bulgarian foreign minister Soloman Passy "welcomed the will of the Ukrainian people to live in a free, open and democratic society".
He appealed to all parties in Ukraine to ensure the re-run election on 26 December "reflects the will of the Ukrainian people".
Delegates disagreed over the planned wording of a final declaration, with Russia objecting to some passages about Ukraine as well as criticism of Russian influence in Georgia and Moldova.
Mr Powell said the US was not competing with any other country for control in Ukraine.
"The people of the Ukraine are playing democracy in the name of freedom," he told the meeting.
"Spheres of influence, I think, is a term that really isn't relevant to the circumstances that we are facing today."
Russian Foreign Minister Sergey Lavrov earlier suggested that the OSCE was guilty of "double standards" when monitoring elections in former Soviet states and more established democracies.
"We must not allow the OSCE monitoring to be turned into a political instrument," he said.
Mr Lavrov emphasised that Moscow hoped the OSCE could focus on practical and economic projects and less on elections and human rights.
Mr Powell added that he disagreed that the OSCE was interfering politically in the former Soviet Union.
The OSCE is discussing whether to nearly double its number of poll monitors in Ukraine to 1,000. Mr Yushchenko is asking for 2,000.