The US has warned Russia that any moves to annex Crimea would close the door to diplomacy.
US Secretary of State John Kerry told his Russian counterpart Sergei Lavrov that Crimea is part of Ukraine and Moscow should avoid military escalation.
Meanwhile, US President Barack Obama has been discussing the deepening crisis with world leaders.
The BBC reports it comes as warning shots were fired as a team of international observers was turned back from entering Crimea.
The Organisation for Security and Co-operation in Europe (OSCE) said that no one was hurt in the incident at Armyansk.
It was the third time the OSCE has been prevented from entering Crimea, now in the control of pro-Russian forces.
Moscow has been tightening its military grip on the Crimean peninsula, and the pro-Russian authorities there have called a 16 March referendum to secede from Ukraine and join Russia.
The exchange between Mr Kerry and Mr Lavrov came in a telephone conversation on Saturday, a US State Department official said.
"He (John Kerry) made clear that continued military escalation and provocation in Crimea or elsewhere in Ukraine, along with steps to annex Crimea to Russia would close any available space for diplomacy, and he urged utmost restraint," the official said.
Russian President Vladimir Putin has insisted he has the right to protect Russian interests and the rights of ethnic Russians in Crimea.
Mr Lavrov had earlier said that the crisis in Ukraine was "created artificially for purely geopolitical reasons". He confirmed that Russia had contacts with Ukraine's interim government but said Kiev was beholden to the radical right.
Speaking to reporters in Moscow on Saturday, he said: "We are ready to continue a dialogue [with the West] on the understanding that a dialogue should be honest and partner-like, and without attempts to make us look like a party to the conflict. We didn't create this crisis."
Calls to national leaders
As diplomatic efforts to resolve the crisis continued, Mr Obama held individual conversations on Saturday with British Prime Minister David Cameron, Italian Prime Minister Matteo Renzi and French President Francois Hollande, the White House said.
"The leaders reiterated their grave concern over Russia's clear violation of international law and reaffirmed their support for Ukraine's sovereignty and territorial integrity," a statement said.
Mr Obama also held a conference call with Latvian President Andris Berzins, Lithuanian President Dalia Grybauskaite and Estonian President Toomas Hendrik Ilves. The three Baltic states were all part of the former Soviet Union.
Earlier, the French presidency said Mr Hollande and Mr Obama discussed "new measures" against Russia if it failed to act to defuse the crisis.
They insisted on the "need for Russia to withdraw forces sent to Crimea since the end of February and to do everything to allow the deployment of international observers," Mr Hollande's office said.
It was not clear what "new measures" could entail.