Ukraine’s interim PM Arseniy Yatsenyuk met President Barack Obama at the White House.
During their meeting, Barack Obama pledged to “stand with Ukraine” in its dispute with Russia.
The US president 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.
Arseniy Yatsenyuk, speaking after meeting Barack 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.
Barack 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, Barack 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”.
The president 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.
Barack Obama also said the US “will completely reject” the results of Crimea’s referendum, saying it had been put together in a “slapdash” way.
As Barack Obama and Arseniy Yatsenyuk were holding talks, the US Senate Foreign Relations Committee voted to authorize $1 billion in loan guarantees to Ukraine’s new government and allow the US to impose sanctions on Russian and Ukrainian officials.
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