The White House has said that Russian President Vladimir Putin called US President Barack Obama to discuss the United States' proposal for diplomatic talks on the issue of Ukraine.
The US has said it is in favour of holding independently mediated talks since the crisis began.
US Secretary of State John Kerry again presented proposals to the Russian Foreign Minister earlier this week.
In a statement, the White House claimed Mr Putin had made contact to discuss these.
Mr Obama said he told Mr Putin this option was only available if Russian troops were pulled back and no further steps were taken to violate Ukraine's sovereignty.
This comes as deposed Ukraine president Viktor Yanukovych has called for referendums to be held across the country to determine the future status of every Ukrainian region, instead of presidential elections planned for May.
Mr Yanukovych said: "As president who is with you in thought and soul, I ask every single sensible citizen of Ukraine not to let yourselves be used by the imposters.
"Demand a referendum on determining the status of every region in Ukraine."
The comments, which were his first in over two weeks, came after Crimea voted to become part of Russia in a referendum earlier this month and was then rapidly incorporated into Russian territory.
Mr Yanukovych fled Ukraine for Russia last month and is now reportedly living in a country house outside Moscow, although his two public appearances since have been in the southern city of Rostov-on-Don.
He said he would not recognise presidential polls that are planned to be held on 25 May and nationwide referendums should be held instead.
"Only a nationwide referendum, and not snap polls, can to a large extent stabilise the political situation and preserve the sovereignty and integrity of Ukraine," he said.
Russian officials, including Mr Putin, have said that Mr Yanukovych remains the legitimate president of Ukraine and have refused to recognise the pro-West rulers who took over after his fall.
However, Mr Putin has also said Mr Yanukovych has no political future and it is not clear to what extent the former president's statements are a reflection of Russian policy.
The Regions Party - the Ukrainian faction that Mr Yanukovych dominated for over a decade - is due to hold a congress to determine its future strategy at the weekend.
The party has recognised that it needs a complete overhaul after the fall and disgrace of its former figurehead and is going to take full part in the presidential elections.
Mr Yanukovych in his statement asked to be removed from the party and relieved of his duties as honorary chairman, a move the congress was expected to make anyway.
Mr Obama earlier had said Russia's troop build-up on the Ukraine border was out of the ordinary and called on Russia to pull its military back and begin talks to defuse tension.
"You've seen a range of troops massing along that border under the guise of military exercises," he told CBS show This Morning in an interview in Vatican City.
"But these are not what Russia would normally be doing."
Mr Obama said the moves might be no more than an effort to intimidate Ukraine, but also could be a precursor to other actions.
"It may be that they've got additional plans," he said.
Hungary opposes economic sanctions on Russia
Earlier, Hungarian Prime Minister Viktor Orban said Hungary is against the European Union imposing a round of economic sanctions on Russia over its intervention in Ukraine.
He was quoted in an interview published by the business daily Vilaggazdasag.
The central European country of ten million people relies on Russia for about 80% of its natural gas needs.
It recently signed a €10bn deal with Russia for Rosatom, Russia's state nuclear corporation, to expand Hungary's Paks nuclear plant, a major power generator.
Russia is also Hungary's largest trading partner outside the European Union, with exports worth €2.55bn in 2013.
"Economic sanctions are in the third round and it would be fortunate to avoid these because it is not in the interests of either Europe, or much less Hungary," Mr Orban was quoted as saying.
Messages over the past week from officials in the EU's 11 ex-communist member states indicated that most are going to resist any attempt by the union to impose the next stage of sanctions on trade and economic ties.
Mr Orban said the crisis in Ukraine and the political sanctions since imposed have not affected Hungary's nuclear deal with Russia so far and that he hoped this would remain the case.
The head of Rosatom said this week that some of its international contracts could be affected by Western sanctions, RIA news agency reported.
Hungary and Slovakia connected their gas networks this week as part of European Union efforts to strengthen supply security in a region of the union heavily dependent on imports from Russia.