The BBC's Daniel Sandford says "what appear to be Russian troops" are standing guard at local government offices in Simferopol
The unofficial pro-Moscow leader of Ukraine's autonomous Crimea region has asked Russian President Vladimir Putin for help to ensure peace.
A Kremlin source said it would "not leave unnoticed" the request from Sergiy Aksyonov.
Reports speak of a clash overnight in Crimea's capital and an attempt to seize a Ukrainian missile base.
Ukraine's interim Prime Minister, Arseniy Yatsenyuk, accused Russia of seeking to provoke an escalation.
He was speaking at the first meeting of his cabinet, installed after the overthrow of President Viktor Yanukovych. New Defence Minister Ihor Tenyukh accused Russia of "recently" deploying 6,000 extra soldiers to Ukraine.
US President Barack Obama warned Moscow against any military intervention as unidentified soldiers, thought to be Russian, fanned out in the south of the peninsula, surrounding airports and communications centres.
According to Mr Aksyonov, soldiers from Russia's Black Sea Fleet based in Crimea are helping to guard strategic buildings. But the fleet's press service only told a Russian news agency Ria-Novosti it would help guard fleet installations.
Under the agreement governing the presence of the fleet in Crimea, the Russians must co-ordinate all troop movements outside the fleet's base areas with the Ukrainian authorities beforehand.
The head of Russia's upper house of parliament, Valentina Matviyenko, said she could not rule out the dispatch of a "limited contingent" of troops to Crimea to "guarantee the security of the Black Sea Fleet and Russian citizens living on the territory of Crimea".
European Commission President Jose Manuel Barroso has said he is shocked by reports of the "violation of Ukraine's sovereignty".
Reports are coming in of big pro-Russian rallies in several Ukrainian cities outside Crimea
- In Donetsk, Mr Yanukovych's traditional stronghold, demonstrators from a crowd of some 7,000 tried unsuccessfully to occupy the regional administration building, raising a Russian tricolour on a nearby flag-post
- In Kharkiv, Ukraine's second-biggest city, scuffles broke out when protesters with Russian flags tried to occupy the regional administration building
- In Mariupol, in the south-east, hundreds of protesters carrying Russian flags gathered outside the city council
Sergiy Aksyonov: "I call on the president of the Russian Federation, Vladimir Putin, to provide assistance in securing peace"
Russia's foreign ministry said several people had been hurt when "unidentified armed people sent from Kiev" tried to seize control of Crimea's interior ministry overnight.
The attempt was rebuffed by "self-defence units", the ministry said in a report which could not be independently confirmed.
According to the Ukrainian news agency Unian, Russian soldiers have been trying to take control of a Ukrainian anti-aircraft missile unit near Yevpatoria, in Crimea.
Ukraine's acting President, Olexander Turchynov, signed a decree on Saturday declaring that the election of Mr Aksyonov as prime minister of Crimea this week was illegal.
Unidentified soldiers are guarding key installations in Crimea
Machine-gunners took up position outside the Crimean parliament
In Donetsk, thousands of pro-Russian demonstrators rallied outside regional government offices
In Kiev, demonstrators remain on Independence Square, where the uprising began
Some turned out in Kiev to sing the national anthem on Saturday
In the same vote which elected him, the Crimean parliament called a referendum on the status of the territory, which is dominated by ethnic Russians.
Mr Aksyonov, who leads the main pro-Russian party in Crimea, brought forward the vote to 30 March, from 25 May - the date of Ukraine's early presidential election.
He also announced he was taking control of security in Crimea "on a temporary basis".
'Escalation'
The new government in Kiev was formed this week by opposition parties and street activists.
Mr Yatsenyuk said: "The presence of Russian soldiers is a provocation and we demand that Russian soldiers return to their permanent bases."
"We are taking no steps that could provoke a violent confrontation," he said. "All responsibility for the escalation of the conflict lies personally at the leadership of the Russian Federation."
Reporting the deployment of Russian soldiers, Defence Minister Tenyukh said that around 30 armoured vehicles had also been deployed in Crimea.
Viktor Yanukovych, who was deposed after months of unrest degenerated into bloodshed this month, made his first appearance in Russia on Friday, insisting he was still the legitimate president of Ukraine.
In his address late on Friday, Mr Obama warned Russia there would be "costs" for any military intervention and commended Ukraine's interim government for its "restraint".
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