The EU and US say plans to hold a referendum in Crimea on whether to break away from the Ukraine and join Russia are illegal.
Officials in the area voted in favour of the move earlier; a referendum in 10 days time.
US President Barack Obama says that would also violate the Ukrainian constitution:
Leaders have been attending an emergency summit in Brussels to discuss the European response to the Ukrainian crisis. Earlier the Crimean parliament announced plans for a referendum next week on whether to break away from Russia entirely.
European Council president Herman van Rompuy has demanded that Russia take its troops out of the region:
The US President Barack Obama has ordered a freezing of US assets and visa restrictions on those involved in Russia's military intervention in Crimea.
Mr. Obama signed an executive order aimed at punishing Russians and Ukrainians responsible for "threatening the sovereignty and territorial integrity of Ukraine".
"This (executive order) is a flexible tool that will allow us to sanction those who are most directly involved in destabilising Ukraine, including the military intervention in Crimea, and does not preclude further steps should the situation deteriorate," the White House said.
Viktor Yanukovych
Russia has claimed Ukraine's ousted president Viktor Yanukovych asked Moscow to send troops to re-establish law and order in his country, but the West has dismissed Moscow's version of events.
Russia's Foreign Minister Sergei Lavrov, who has met for a second round of talks with US Secretary of State John Kerry, says US sanctions against Russia are "not constructive".
Meanwhile, Interpol says it's received a request for an international arrest warrant to be issued for the deposed Ukrainian president.
Officials in Kiev want him on charges of abuse of power and murder.
Ukrainian PM Arseniy Yatsenyuk & President of the European Council Herman Van Rompuy
It comes as Crimea's deputy prime minister Rustam Temirgaliev says a decree making the region part of Russia is already in place.
Mr. Temirgaliev said "The only lawful armed force on the territory of the Crimea is the Russian armed forces".
MPs in the southern Ukrainian region, who have voted in favour of becoming part of Russia, are now calling for a referendum in 10 days, but the government in Kiev says the move is unconstitutional.
Ukrainian Prime Minister Arseniy Yatsenyuk, who has been meeting European leaders in Brussels, says Crimean will remain a part of Ukraine.
Mr. Yatsenyuk said earlier the conflict is not just between Ukraine and Russia but one of huge concern for all of Europe.
The US has been particularly critical of the Russian President. Former Secretary of State Hillary Clinton has compared President Putin's claims to the Nazis in Germany.
It comes after US Secretary of State John Kerry failed in an attempt to get Russian Foreign Minister Sergei Lavrov and the Ukraine interim Foreign Minister Andriy Deshchytsya to sit down for talks in Paris yesterday. However, Mr. Kerry says he will not give up on finding a diplomatic solution.
In Simferopol, Crimea's capital, about 50 people rallied outside the parliament waving Russian and Crimean flags. Among the posters they held was one that said "Russia, defend us from genocide."
There are concerns the turmoil may engulf eastern Ukraine after hundreds of protesters - many chanting "Russia! Russia!" - stormed a government building in Donetsk, a major industrial centre near the Russian border.
Clashes between protesters and police broke out early on Thursday as police cleared demonstrators from the building. Dozens of people have been detained.
Around 40 unarmed military personnel are expected in Crimea in a mission by the Organisation for Security and Co-operation in Europe to try to defuse tensions in region.
The UN special envoy to Crimea Robert Serry was forced to cut short a visit on Wednesday when he was confronted by unidentified gunmen.
Meanwhile a US-based anchor for the Russia Today television network resigned live on air in protest at Russia's actions in Ukraine.
