* Armed men seize buildings in Crimea, run up Russian flag
* Acting president warns Moscow against Crimea troop moves (Adds seizure of airport, U.S. vice president's call to Ukraine prime minister in paragraph 7)
By Alessandra Prentice and Alissa de Carbonnel
SIMFEROPOL, Ukraine, Feb 28 (Reuters) - The United States told Russia to demonstrate in coming days that it was sincere about its promise not to intervene in Ukraine as armed men stormed the regional parliament and hours later others seized the airport in a mainly ethnic Russian region.
Crimea, the only Ukrainian region with an ethnic Russian majority, is the last big bastion of opposition to the new leadership in Kiev since pro-Russian President Viktor Yanukovich was ousted at the weekend.
The region also provides a base for the Russian navy's Black Sea Fleet. Kiev's new rulers said any movement by Russian forces beyond the base's territory would be tantamount to aggression.
U.S. Secretary of State John Kerry said Russian Foreign Minister Sergei Lavrov had assured him by telephone that Moscow would not intervene militarily in its neighbour.
"We believe that everybody now needs to take a step back and avoid any kind of provocations," Kerry said at a joint news conference with German Foreign Minister Frank-Walter Steinmeier.
"We want to see in the next days ahead that the choices Russia makes conform to this affirmation we received today."
The United States pledged its support for the new government in a call on Thursday by Vice President Joe Biden to Ukrainian Prime Minister Arseny Yatseniuk.
Yanukovich, who fled Kiev after scores of demonstrators were killed last week, was expected to hold a news conference in Russia on Friday. He has declared he is still Ukraine's president, but has lost support even in regions where the ethnic Ukrainian population mainly speaks Russian as he does.
Crimea, which was administered as part of Russia within the Soviet Union until it was transferred to Ukraine in 1954, is a more tendentious question. Separatism there has often flared up at times of tension between Moscow and Kiev.
A group of armed men in military uniforms seized the main regional airport in Simferopol, Crimea, Interfax news agency said early on Friday.
A day before, unidentified gunmen seized the Crimean parliament and raised a Russian flag. The gunmen issued no demands and police hardly seemed to treat the event as a major security incident.
Instead, they casually guarded the building while hundreds of pro-Russian demonstrators assembled, including elderly people who danced cheerfully to recordings of Soviet martial music.
The regional parliament even managed to hold a session inside the building on Thursday despite the siege, where it voted to stage a referendum on "sovereignty" for Crimea.
By the early hours of Friday, police guarding the building would not say what had happened to the gunmen or whether they were even still there. Russia's flag still flew from its roof and lights were on in the windows of its top floor.
Oleksander Turchinov, Ukraine's acting president, warned Russia not to move personnel beyond areas permitted by treaty for those using its naval base: "Any military movements, the more so if they are with weapons, beyond the boundaries of this territory will be seen by us as military aggression," he said.
Russia has repeatedly declared it will defend the interests of its citizens in Ukraine, and on Wednesday announced war games near the border involving 150,000 troops on high alert. Kerry said Lavrov told him the war games were pre-planned.
Although Moscow says it will not intervene by force, its rhetoric since the removal of its ally Yanukovich has echoed the runup to its invasion of Georgia in 2008, when it sent its troops to protect two self-declared independent regions and then recognised them as independent states.
Witness accounts suggest those who captured the Crimean parliament building in the early hours of Thursday were pro-Russian gunmen of some kind.
"We were building barricades in the night to protect parliament. Then this young Russian guy came up with a pistol ... we all lay down, some more ran up, there was some shooting and around 50 went in through the window," Leonid Khazanov, an ethnic Russian, told Reuters.
"I asked them what they wanted, and they said 'To make our own decisions, not to have Kiev telling us what to do'."
Ukraine's new interior minister, Arsen Avakov, said the attackers had automatic weapons and machine guns.
The regional prime minister said on Thursday he had spoken to the people by telephone, but they had not made any demands or said why they were there. They had promised to call him back but had not done so, he said.
With the siege apparently still under way, the regional parliament met in another part of the building and voted to hold its referendum on May 25, the day Ukraine plans to elect a new president to replace Yanukovich. The measure, if passed, would declare Crimea sovereign, with its relationship to the rest of Ukraine governed by treaty.
The pro-Russian crowd outside cheered the news.
"In three months we will have a chance to choose our future," said Yuri Lukashev, 58, a carpenter standing in a group of other ethnic Russian men outside the building late at night. "We're celebrating our victory. It's a chance for peace in Crimea, guaranteed by Russia."
However, elsewhere there was some anger at the invasion of the regional parliament and the flying of the Russian flag.
Alexander Vostruyev, 60, in a leather cap and white beard, said: "It's disgrace that the flag of a foreign country is flying on our parliament ... It's like a man coming home to find his wife in bed with another man." (Writing by Peter Graff; Editing by Bernard Orr and Lisa Shumaker)