Secretary of State John Kerry said he had spoken to his Russian counterpart who promised to respect Ukraine’s “territorial integrity”.
But he warned Moscow needed to back up its words with actions.
Earlier, pro-Russian armed men stormed Crimea’s local parliament, while Russia has been conducting military exercises.
The ousted Ukrainian President, Viktor Yanukovych, who is on the run since he was voted out of office last week, also reportedly surfaced in Russia.
Ukrainian media said he arrived in the southern Russian city of Rostov-on-Don early on Friday, where he is due to give a news conference.
The news website Ukrayinska Pravda reports that there were four Kamaz trucks and around 150 armed men, some speaking with “thick Russian accents”.
However the airport was reportedly working as normal. One unnamed source at the airport told Russia’s Ria Novosti news agency that the report it had been seized “does not correspond to reality”.
In a separate incident on Thursday, unidentified armed men entered Crimea’s parliament building by force and hoisted a Russian flag on the roof.
They were cheered by a handful of pro-Russian demonstrators who gathered round the building, despite a police cordon.
“We’ve been waiting for this moment for 20 years,” the protest leader said. “We want a united Russia.”
The men are believed to be still in the building, although it is not clear if they have made any demands or statements.
They did put up a sign reading “Crimea is Russia” and threw a flash grenade in response to questions from a journalist, AP news agency reported.