Leaders of the G7 group of nations have called on Russia to stop all efforts to "annex" Ukraine's Crimea region.
They said if Russia took such a step they would "take further action, individually and collectively".
The G7 leaders also said they would not recognise the results of a referendum in Crimea this weekend on whether to split from Ukraine and join Russia.
Separately, the US president said they "will be forced to apply costs" if Russia does not change course.
Barack Obama was speaking after holding talks with Ukraine's interim Prime Minister Arseniy Yatsenyuk in Washington.
Mr Yatsenyuk told reporters Ukraine "is and will be part of the Western world".
Earlier, Ukraine's national security chief Andriy Parubiy warned of a major Russian military build-up on Ukraine's borders.
He said Russian troops had not withdrawn since carrying out military exercises near Ukraine's eastern and southern frontiers last month, and were now "only two to three hours" from Kiev.
The Group of Seven industrial nations - Britain, Canada, France, Germany, Italy, Japan and the US - along with the European Union urged Russia to "cease all efforts to change the status of Crimea".
"In addition to its impact on the unity, sovereignty and territorial integrity of Ukraine, the annexation of Crimea could have grave implications for the legal order that protects the unity and sovereignty of all states," they said in a statement released by the White House.
They said Sunday's referendum, asking the people of Crimea if they want to be a part of Russia or Ukraine, has "no legal effect" as it is in "direct violation" of Ukraine's constitution.
"Given the lack of adequate preparation and the intimidating presence of Russian troops, it would also be a deeply flawed process which would have no moral force," they added.
The G7 leaders repeated their calls for Russia to de-escalate the crisis by withdrawing its troops, talking directly with Kiev and using international mediators to "address any legitimate concerns it may have".
European Commission President Jose Manuel Barroso said he hoped EU countries would keep their "very united and firm position because we don't want to see, one century after the First World War, exactly the same kind of behaviour of countries annexing other countries".
Polish PM Donald Tusk said it may be time for the EU "to consider the possibility of having second phase sanctions" against Russia.
At a joint news conference with Mr Tusk, German Chancellor Angela Merkel indicated the EU could sign the "political part" of a long-awaited agreement on closer ties with Ukraine later this month.
But diplomatic efforts with Russia continue.
US Secretary of State John Kerry said he will travel to London for talks with Russian Foreign Minister Sergei Lavrov on Friday, and present him "with a series of options" for resolving the crisis.
France's President Francois Hollande has spoken by telephone to Russia's President Vladimir Putin, and both agreed to "continue the discussion" on resolving the crisis.
Russian troops and pro-Russian gunmen moved in to seize key sites in Crimea - an autonomous region with a majority of ethnic Russians - after the fall of Ukraine's President Viktor Yanukovych last month.
Andriy Parubiy said Russian troops had been seen massing on Ukraine's eastern and southern borders where he said there was a "critical situation".
He accused Moscow of sending "subversive agents" into those areas to try to create a pre-text to deploy troops in the same way it has done in Crimea.
Mr Parubiy said Kiev's parliament will vote on Thursday to establish a National Guard of 20,000 people - recruited from activists involved in the recent pro-Western protests as well as from military academies - to strengthen Ukraine's defences.
The National Guard, he said, would be deployed to "protect state borders, general security and prevent "terrorist activities".
President Yanukovych was forced from office after violence broke out between police and protesters in Kiev, in which more than 90 people were killed.
The protesters had taken over Kiev's Independence Square, calling for the government's resignation, after Mr Yanukovych rejected a deal with the EU in favour of a bail-out from Russia.