Pro-Russian demonstrators have pushed through police lines in Simferopol, says Mark Lowen
Ukrainian interim President Olexander Turchynov has warned Russia against any "military aggression" in Crimea.
He said Russia's troops from Russia's Black Sea Fleet should not move outside their naval base in Sevastopol.
The warning comes after unknown armed men seized Crimea's regional parliament and the government headquarters of the autonomous Russian-majority region.
Meanwhile, the Crimean parliament has said it wants to hold a referendum on greater self-rule.
Such a vote would be a challenge to the new powers in the Ukraine capital Kiev, the BBC's Mark Lowen reports from the Crimean regional capital Simferopol.
'Miscalculation'Prime Minister Arseniy Yatsenyuk told the BBC: "We ask our Russian partners to... stick to their obligations, we believe Russia would never intervene into Ukrainian domestic affairs and will refrain from any steps that would split Ukraine.
"We are committed to having Ukraine as one united country. We will punish anyone for separatism in Ukraine with all legal and constitutional means," he added.
Mr Yatsenyuk was confirmed as prime minister in a parliamentary vote on Thursday afternoon. He is a key ally of former Prime Minister Yulia Tymoshenko, who was released from detention last week.
Watch a short history of the Republic of Crimea
The warnings from Ukrainian leaders came as Russia performed a second day of military exercises, saying its fighter jets were on "combat alert".
"Constant air patrols are being carried out by fighter jets in the border regions," Russia's defence ministry told Interfax.
On Wednesday, President Vladimir Putin ordered a snap drill to test the combat readiness of troops in central and western Russia, near the border with Ukraine. Thursday's exercises appear to be part of that drill, analysts say.
The Russian foreign ministry expressed concern over what it termed "massive violations of human rights in Ukraine".
Amid heightened tensions between Russia and the West, Nato Secretary General Anders Fogh Rasmussen said he was "concerned about developments in Crimea" and urged Russia "not to take any action that can escalate tension".
US Defense Secretary Chuck Hagel gave a similar warning after Nato talks in Brussels, telling Russia "not to take any steps that could be misinterpreted, or lead to miscalculation, during a very delicate time".
A crowd of pro-Russian protesters gathered outside the parliament building in Simferopol after it was seized by armed men
Police were deployed around the building
The Russian flag has been raised over the building
On Wednesday there were clashes between pro- and anti-Russian protesters in SimferopolAlso on Thursday, former President Viktor Yanukovych issued his first statement since being voted out of office by MPs last week, telling Russian news agencies he had been "compelled to ask the Russian Federation to ensure my personal security from the actions of extremists" and that he still considered himself the legitimate president of Ukraine.
The state-run Itar-Tass agency quoted an official source as saying Mr Yanukovych would be granted "protection" by Russia, although there was no official confirmation of this.
'Provocateurs'
The incident in Simferopol is another illustration of tensions in the region, says the BBC's Mark Lowen in Crimea.
One eyewitness Leonid Kazanov, who saw the unknown armed men entering the parliament building, told local TV: "I asked one of the guys who they were. The guy, who introduced himself only as Andrey, said: 'We are Russia.'"
Mr Kazanov added the attackers acted quickly and efficiently, and were well armed.
Shortly after, the Russian flag was raised over both parliament buildings.
Ukrainian Interior Minister Arsen Avakov said the area near the government buildings has been cordoned off to prevent "bloodshed". He added that the seizure of the buildings was the work of "provocateurs".
"Measures have been taken to counter extremist actions and not allow the situation to escalate into an armed confrontation in the centre of the city," he said in a statement on his Facebook page.
Regional Prime Minister Anatoliy Mohylyov told a local TV station said he would take part in talks with the gunmen and told government employees who normally worked there not to come in.
The men have not yet made any demands or issued any statements but did put up a sign reading: "Crimea is Russia".
They threw a flash grenade in response to questions from a journalist, AP news agency reported.
Separatism fearsTensions have been rising in Crimea since Mr Yanukovych was ousted last week.
On Wednesday the city saw clashes erupt between Ukrainians who support the change of government and pro-Russians.
Crimea - where ethnic Russians are in a majority - was transferred from Russia to Ukraine in 1954.
Ethnic Ukrainians loyal to Kiev and Muslim Tatars - whose animus towards Russia stretches back to Stalin's deportations during World War II - have formed an alliance to oppose any move back towards Moscow.
Russia, along with the US, UK and France, pledged to uphold the territorial integrity of Ukraine in a memorandum signed in 1994.
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