The letter said: "Under the influence of Western countries, there are open acts of terror. I would call on the president of Russia, Mr Putin, to use the armed forces of the Russian Federation to establish peace and defend the people of Ukraine.”

^{Military personnel, believed to be Russian, walk outside the Ukrainian military base in Perevalnoye, Crimea (Reuters)}

Barack Obama and other senior American figures led a renewed round of international condemnation. However, the capacity of European leaders to react decisively has been hampered by the dependence of much of the European Union on Russian oil and gas. Any economic stand-off could derail Europe’s fragile economic recovery.

On Monday the FTSE-100 index of Britain’s leading companies fell by 1.49 per cent and the German stock market by more than 3 per cent. The value of the pound also fell, while natural gas prices rose by almost 10 per cent.

Mr Obama said that Russia was on the "wrong side of history”, and David Cameron said that the West would use "diplomatic, political and economic pressures” on Moscow.

^{Barack Obama speaks about the situation in Ukraine during a meeting with Benjamin Netanyahu (Reuters)}

However, a document photographed in Downing Street suggested that Britain is concerned about the economic impact of any sanctions against Russia. The paper states that the "UK should not support, for now, trade sanctions … or close London’s financial centre to Russians”.

The document also stated that Britain would not support any Nato military preparations and said that the United Nations rather than the EU should take the lead in sending observers to Ukraine. It suggested that ministers were instead considering a more cautious approach including visa restrictions and travel bans on key Russian figures.

The document, which was being carried by Hugh Powell, the deputy national security adviser, is likely to prove embarrassing to the Prime Minister at a time when the Americans are seeking to increase pressure on the Russian president.

John Kerry, the US Secretary of State, is expected to travel to Kiev today. On Monday, Mr Obama said: "I think the world is largely united in recognising the steps Russia has taken are a violation of Ukrainian sovereignty; a violation of international law.”

The president said he had warned Russia that if it continued on its "current trajectory”, it would face "a whole series” of economic and diplomatic steps that would leave it isolated.

However, there was little sign that the increased pressure was doing anything to deter Mr Putin, who continues to insist that he is acting to protect the rights of Russians in Ukraine.

^{A woman kisses a Ukrainian serviceman through the gate by a military unit near an airfield in Crimea (Reuters)}

Ukraine ordered full mobilisation of its forces as bases in Crimea were surrounded and airports and ports occupied by Russian troops. No shots were fired, but according to reports, Alexander Vitko, the commander of Russia’s Black Sea fleet, told Ukrainian forces in Crimea to surrender by 5am (3am GMT) or face a "storm”. The Russian defence ministry insisted that reports of an ultimatum were"nonsense”. Pro-Russian troops also took over Kerch, a ferry terminal on the easternmost tip of the peninsula, intensifying concerns that Moscow is preparing for a further military advance. The terminal is about 12 miles by sea from Russia and serves as a departure point for many Russia-bound ships.

Pro-Russian supporters also took over government buildings in several eastern Ukrainian cities and there were reports of Russian military exercises close to the border.

Despite the international outcry and the rouble hitting record lows, Moscow remained defiant. Sergei Lavrov, the foreign minister, said that troops would remain in Ukraine until the "normalisation of the political situation”, adding: "Violence of ultra-nationalists threatens the lives and the regional interests of Russians and the Russian-speaking population.

"This is a question of defending our citizens and compatriots and ensuring human rights and the right to life.”

In Moscow, the parliament on Monday began debating a law that would oblige the government to seek to annexe any neighbouring region with predominantly Russian ethnicity that votes to join Russia, a situation that may arise in Crimea after a planned referendum later this month.

The EU condemned "acts of aggression” against Ukraine and called for troops to be ordered back to their barracks.

Angela Merkel, the chancellor of Germany, told Mr Obama during a telephone call that after speaking with Mr Putin she was convinced that he was in "another world”.

European leaders have called an emergency summit in Brussels on Thursday to discuss the crisis.

Baroness Ashton, the EU’s foreign policy chief, said: "We need to see a return to barracks by those troops who have currently moved [from where they have been staying]. There are serious concerns about reports of troops and armed personnel moving.”

William Hague, the Foreign Secretary, described Russia’s aggression in Ukraine as the "biggest crisis” which has faced Europe in the 21st century.

Mr Hague, who is in Kiev, has urged Russia to back off from its intervention in Crimea. He said Moscow should be in no doubt that it faced "significant costs” for "taking control” of the Ukrainian region.

Mr Hague told the BBC Radio 4 Today programme there was a "constant risk” of a "flashpoint” in Crimea which could send the situation out of control.

He praised the Ukrainian government for showing restraint despite the "provocation”, and said he was "very concerned” about action by Russia in other parts of the country.

Late on Sunday, the G7 of major industrialised powers also condemned Moscow’s military build-up and condemned "the Russian Federation’s clear violation of the sovereignty and territorial integrity of Ukraine”.

It added: "We have decided for the time being to suspend our participation in activities associated with the preparation of the scheduled G8 Summit in Sochi in June.”

G7 finance ministers said they were ready "to provide strong financial backing to Ukraine”.