LONDON (REUTERS) - Russia will face serious consequences for President Vladimir Putin's "completely unacceptable" attempt to annex Ukraine's Crimea region, Prime Minister David Cameron said on Tuesday.

"The steps taken by President Putin today to attempt to annex Crimea to Russia are in flagrant breach of international law and send a chilling message across the continent of Europe,"Cameron said in a statement.

"It is completely unacceptable for Russia to use force to change borders, on the basis of a sham referendum held at the barrel of a Russian gun.

"President Putin should be in no doubt that Russia will face more serious consequences and I will push European leaders to agree further EU measures when we meet on Thursday," he said.