US Secretary of State John Kerry has said Ukraine is not caught in a battle between East and West.
Kerry said it was not a zero-sum game and called for all nations to work together to bring stability to Ukraine.
The new administration in Kiev is facing continuing opposition from Ukraine's Russian-speaking regions.
Russia, which backed ousted President Viktor Yanukovych, has warned other states against seeking "unilateral advantages" in Ukraine.
However, Foreign Minister Sergei Lavrov said Russia's "policy of non-intervention" would continue.
On Tuesday, Kerry met British Foreign Secretary William Hague in Washington for talks on the situation in Ukraine.
"Both of us are committed to doing our part to support the efforts of the people of Ukraine who have spoken out on their own with passion for their ability to have a democratic future," Kerry said after the meeting.
"This is not a zero-sum game, this is not West versus East. It is not Russia or the United States, this is about the people of Ukraine and Ukrainians making their choices about the future and we want to work with Russia and other countries, with everybody available, to make sure this is peaceful from this day forward."
Earlier, Ukraine's interim President Olexander Turchynov expressed concern about what he called the serious threat of separatism following the ousting of Yanukovych.
Addressing parliament, he said he would meet law enforcement agencies to discuss the risk of separatism in regions with large ethnic Russian populations. Separatism was a "serious threat", he said.
Many Russian-speaking residents in the south and east of Ukraine have protested against the actions of the interim authorities.
In the Crimean port city Sevastopol on Tuesday, some replaced the Ukrainian flag on a local government building with a Russian flag.
Meanwhile, parliament in Kiev has delayed the formation of a unity government until Thursday.
The delay was to allow further consultations, Turchynov said, adding that "a coalition of national faith must be elected".
Yanukovych fled Kiev at the weekend and his whereabouts are still unknown.
Russian armoured personnel carrier on a street in Sevastopol, Crimea. 25 Feb 2014
Interim authorities have issued a warrant for his arrest and on Tuesday parliament voted in favour of trying him at the International Criminal Court (ICC) in The Hague.
The fugitive president is accused of being behind the deaths of more than 100 protesters at the hands of riot police.
Russia has been strongly opposed to the changes in Ukraine, with Prime Minister Dmitry Medvedev saying on Monday that those behind the new administration had conducted an "armed mutiny".
Lavrov said it was in Russia's interests for Ukraine "to be part of the broad European family" but against Russia's interest to "allow the radicals and nationalists who are clearly trying to take centre stage to prevail."
Unrest in Ukraine began in November when Yanukovych rejected a landmark association and trade deal with the EU in favour of closer ties with Russia.
Ukraine is close to bankruptcy and with promised loans from Russia looking increasingly unlikely, interim leaders are looking to the West to bail the country out.
EU foreign affairs chief Catherine Ashton held further talks in Kiev on Tuesday to discuss financial and political support for Ukraine's new leaders.
She urged the provisional authorities to include Yanukovych supporters in any new government, adding: "Everyone I've spoken to here recognises the importance of this country sticking together. But we also know that there are big financial and economic challenges in the days, weeks and months ahead."