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
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 lengthy overnight talks.
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 sticking points are the question of constitutional reforms and opposition demands to sack the government.
The stand-off paves the way for a stormy parliamentary debate on Tuesday.
The six hours of talks in Kiev, 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 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 Mr Powell - speaking to foreign ministers of the Organisation for Security and Co-operation in Europe (OSCE) - said the US was not competing with any other country for control.
"The people of the Ukraine are playing democracy in the name of freedom," he told the meeting in the Bulgarian capital Sofia.
"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 emphasised Moscow's desire to see the OSCE more focused on practical and economic projects and less on elections and human rights, but Mr Powell said an expanded agenda should never be at the expense of such things.
He added that he disagreed that the OSCE was interfering politically in the former Soviet Union.
Its member nations had signed up to the idea that freedom, democracy and the rule of law were of universal concern, he said.
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.
Monday's talks in Kiev represented the first time since the supreme court ruling that the two rivals had sat down together to negotiate.
President Kuchma announced that both sides had agreed on key opposition demands to reform electoral rules and appoint a new electoral commission.
Yanukovych wants to prove he has majority support
But he refused to sack the government - another key opposition demand - even though it lost a parliamentary no-confidence vote last week.
The two sides also failed to agree constitutional reforms to weaken the powers of the president, a move favoured by Mr Kuchma.
But Mr Yuschenko - who believes he was the rightful winner of November's poll - says they would leave the president as a mere figurehead.
The opposition has said that unless all its demands are met, the street protests that have lasted for more than two weeks will continue.
Mr Yanukovych vowed on Monday to contest the re-run of the disputed poll, saying he had come under pressure to withdraw.
He said he had the support of millions of Ukrainians and was confident of winning, adding that he was going to take time off from government for the campaign.