US President Barack Obama has welcomed Ukraine’s interim prime minister to the White House and pledged to “stand with Ukraine” in its dispute with Russia.
He warned Russian President Vladimir Putin the international community “will be forced to apply costs” if Russia does not remove its troops from Crimea.
Earlier, leaders of the G7 group of nations issued a similar threat.
Ukraine PM Arseniy Yatsenyuk, speaking after meeting Mr Obama, said Ukraine “will never surrender” to Russia.
“It is absolutely unacceptable to have Russian boots on the Ukrainian ground in the 21st century, violating all international deals and treaties,” he said.
The diplomatic appeals to Moscow come ahead of Sunday’s referendum in Crimea, in which citizens will be asked if they want to stay with Ukraine or join Russia.
The Russian military and pro-Russian armed men moved in to seize key sites in Crimea – an autonomous region of Ukraine whose population is mainly ethnic Russian – in late February after the fall of President Viktor Yanukovych.
President Obama said the US has “been very clear that we consider Russia’s incursion into Crimea outside of its bases to be a violation of international law”.
“We have been very firm in saying we will stand with Ukraine and the Ukrainian people in ensuring that territorial integrity and sovereignty is maintained,” he added.
In reference to scheduled talks between US Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov in London on Friday, Mr Obama said he hoped diplomatic efforts will result in a “rethinking of the process”.
But he stressed that if Moscow “continues on the path that it is on then, not only us, but the international community… will be forced to apply a cost to Russia’s violations of international law and its encroachments on Ukraine”.
He did not specify what those costs would be, but Washington has already issued visa bans to some high-profile Russians and threatened asset freezes for others.
Mr Obama also said the US “will completely reject” the results of Crimea’s referendum, saying it had been put together in a “slapdash” way.
This was a very public show of America’s support for the interim Ukrainian government, the BBC’s Rajini Vaidyanathan reports from Washington.
The BBC’s John Simpson says the vote “won’t affect anything in the longer run”
But it is still unclear what, if anything, will force Russia to change course, she adds.
As Mr Obama and Mr Yatsenyuk were holding talks, the US Senate Foreign Relations Committee voted to authorise $1bn in loan guarantees to Ukraine’s new government and allow the US to impose sanctions on Russian and Ukrainian officials.
Earlier, the leaders of the G7 group of industrial nations – Britain, Canada, France, Germany, Italy, Japan and the US – and the EU issued a similar statement out of Washington.
They threatened to “take further action, individually and collectively” if Russia continues on its course.
At a joint news conference in Warsaw, German Chancellor Angela Merkel and Polish Prime Minister Donald Tusk said EU foreign ministers could discuss “a second stage of sanctions” when they meet on Monday.
EU leaders have already suspended talks with Russia on easing visa restrictions as well as preparations for a G8 meeting in Sochi in June.
Mrs Merkel also indicated the EU could sign the “political part” of a long-awaited agreement on closer ties with Ukraine later this month.
Ukraine’s national security chief Andriy Parubiy has 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.
And he also 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”.
Tensions have been high since President Yanukovych fled Ukraine for Russia on 22 February following days of violent clashes between police and protesters in Kiev, in which more than 90 people were killed.
The protesters had been in Kiev’s Independence Square since November, in protest at Mr Yanukovych’s decision to reject a deal with the EU in favour of a bail-out from Russia.