Armed self-defence groups are reported to be forming across Ukraine's automous republic of Crimea, as several government buildings were seized in the capital, Simferopol.
Russian flags are flying over the regional Parliament and government headquarters.
The seizure came as Russia put 150,000 troops on high alert on the border with Crimea, where most people align with their neighbour rather than the West.
The door of the parliament in the Crimean capital, Simferopol, has been blockaded from inside with tables and chairs and no one is able to enter.
Interfax news agency quoted a witness as saying there were about 60 people inside and that they had many weapons.
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 ousting of President Viktor Yanukovich on Saturday.
Ukraine's new leaders had been voicing alarm over signs of separatism in Crimea, where thousands of pro-Russia separatists tussled with supporters of the country's new leaders.
One person died, apparently of a heart attack, and two were trampled and injured when people stumbled and fell to the ground in the crush.
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.
The change of government in Kiev has raised questions over the future of Russia's naval bases in the Crimean port city of Sevastopol, the lease for which was extended until 2042 by Mr Yanukovych.
Most analysts believe the new leadership will not push for the withdrawal of the Russian fleet, as that could further threaten Ukraine's internal stability as well as the country's fragile relations with Russia.
Putin orders drill near border
Coincidentally, the Russian president, Vladimir Putin, has unexpectedly ordered a military drill to test the combat-readiness of armed forces across western Russia, near Ukraine.
The order appears to be in response to conflicts between pro- and anti-Russian groups in Ukraine, which have arisen since the pro-Russian Mr Yanukovych was ousted at the weekend.
US secretary of state John Kerry has warned Russia it would be a "grave mistake" to embark on any military intervention.
Welcome to hell
Ukraine's new prime minister-designate has just accepted the job with the words: "We are on the brink of a disaster and this is the government of political suiciders! So welcome to hell."
The Maidan council has named Fatherland Party leader Arseniy Yatsenyuk to become prime minister and lead the cabinet until early presidential elections on 25 May.
The cabinet - to be voted on by MPs on Friday - includes leading activists from the three months of demonstrations that finally toppled President Viktor Yanukovych.
The council - made up of protester groups and activists - announced its nominations at a big gathering of protesters at the camp spread over Kiev's Independence Square.
Mr Yatsenyuk - a former speaker of parliament and foreign minister - has been one of the main opposition leaders during the protests.
"We are to undertake extremely unpopular steps as the previous government and previous president were so corrupted that the country is in a desperate financial plight," he told the BBC.
"We are on the brink of a disaster and this is the government of political suiciders! So welcome to hell."
The key foreign affairs ministry portfolio goes to Andriy Deshchytsia, who played a key role in rallying diplomats in support of the protests. Overall Maidan commander Andriy Parubiy - who commands huge respect among the protesters - was named candidate for secretary of the National Security and Defence Council.
Tetyana Chornovol and Dmytro Bulatov - prominent activists who were badly beaten by unknown attackers earlier this year - are set to head the anti-corruption bureau and the ministry of youth and sports respectively.
Yanukovych 'still in Ukraine'
Meanwhile, Mr Yanukovych has been put on the international wanted list, the BBC reports. The fugitive leader is accused of being behind the deaths of more than 100 protesters at the hands of riot police.
But despite rumours that Mr Yanukovych - who fled Kiev at the weekend - is now in Russia, deputy general prosecutor Mykhailo Holomsha told reporters: "We have information indicating Yanukovych is still in Ukraine."