"I am appealing to the military leadership of the Russian Black Sea fleet," said Olexander Turchinov, acting president since the removal of Viktor Yanukovich last week. "Any military movements, the more so if they are with weapons, beyond the boundaries of this territory (the base) will be seen by us as military aggression
Ukraine's Foreign Ministry also summoned Russia's acting envoy in Kiev for immediate consultations.
There were mixed signals from Moscow, which put fighter jets along its western borders on combat alert, but earlier said it would take part in discussions on an International Monetary Fund (IMF) financial package for Ukraine. Ukraine has said it needs $35 billion over the next two years to stave off bankruptcy.
The fear of military escalation prompted expressions of concern from the West, with NATO Secretary General Anders Fogh Rasmussen urging Russia not to do anything that would "escalate tension or create misunderstanding".
Polish foreign minister Radoslaw Sikorski called the seizure of government buildings in the Crimea a "very dangerous game".
"This is a drastic step, and I'm warning those who did this and those who allowed them to do this, because this is how regional conflicts begin," he told a news conference.
It was not immediately known who was occupying the buildings in the regional capital Simferopol and they issued no demands, but witnesses said they spoke Russian and appeared to be ethnic Russian separatists.
Interfax news agency quoted a witness as saying there were about 60 people inside and they had many weapons. It said no one had been hurt when the buildings were seized in the early hours by Russian speakers in uniforms that did not carry identification markings.
"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.
"They're still there ... Then the police came, they seemed scared. I asked them (the armed men) what they wanted, and they said 'To make our own decisions, not to have Kiev telling us what to do'," said Khazanov.
About 100 police were gathered in front of the parliament building, and a similar number of people carrying Russian flags later marched up to the building chanting "Russia, Russia" and holding a sign calling for a Crimean referendum.
One of them, Alexei, 30, said: "We have our own constitution, Crimea is autonomous. The government in Kiev are fascists, and what they're doing is illegal ... We need to show our support for the guys inside (parliament). Power should be ours."
Crimea, the only Ukrainian region with an ethnic Russian majority, is the last big bastion of opposition to the new political leadership in Kiev following the ouster of Yanukovich on Saturday.
Part of Russia's Black Sea fleet is based in Crimea, in the port of Sevastopol
Ukraine's new leaders have been voicing alarm over signs of separatism there. The seizure of the building was confirmed by acting interior minister Arsen Avakov, who said the attackers had automatic weapons and machine guns.
"Provocateurs are on the march. It is the time for cool heads," he said on Facebook.
Turchinov, speaking in Kiev to parliament, which had been called to name a new government, described the attackers as "criminals in military fatigues with automatic weapons".
He also called on Moscow not to violate the terms of an agreement that gives the Russian Black Sea fleet basing rights at Sevastopol until 2042.
The regional prime minister said he had spoken to the people inside the building by telephone, but they had not made any demands or said why they were inside. They had promised to call him back but had not done so, he said.
Russian President Vladimir Putin has ignored calls by some ethnic Russians in Crimea to reclaim the territory handed to then Soviet Ukraine by Soviet Communist leader Nikita Khrushchev in 1954.
The United States says any Russian military action would be a grave mistake.
But Russia's foreign ministry said in a statement that Moscow would defend the rights of its compatriots and react without compromise to any violation of those rights.
It expressed concern about "large-scale human rights violations", attacks and vandalism in the former Soviet republic.
Ethnic Tatars who support Ukraine's new leaders and pro-Russia separatists had confronted each other outside the regional parliament on Wednesday.
Yanukovich was toppled after three months of unrest led by protesters in Kiev. He is now on the run and being sought by the new authorities for murder in connection with the deaths of around 100 people during the conflict.
Crimea is the only region of Ukraine where ethnic Russians are the majority, though many ethnic Ukrainians in other eastern areas speak Russian as their first language.
The Tatars, a Turkic ethnic group, were victimised by Soviet dictator Josef Stalin in World War Two and deported en masse to Soviet Central Asia in 1944 on suspicion of collaborating with Nazi Germany.
Tens of thousands of them returned to their homeland after Ukraine gained independence with the collapse of the Soviet Union at the end of 1991.