Russian politician Andrei Lugovoi, wanted by UK police for the murder of Alexander Litvinenko, will be arrested if he enters any European country.
Andrei Lugovoi was recently elected as a Russian MP
The British ambassador to Moscow, Sir Anthony Brenton, said a European arrest warrant had been issued.
Russia's Foreign Minister Sergei Lavrov has blamed the UK for a diplomatic rift which developed after Mr Litvinenko was poisoned in London last year.
He has ordered the closure of two British Council offices in Russia.
The council is a non-governmental organisation which promotes British culture abroad.
Moscow has made it clear that the decision to close the offices in St Petersburg and Yekaterinburg was part of the continuing dispute over its refusal to extradite Mr Lugovoi, a former KGB agent.
Britain expelled four Russian diplomats in July, with Russia expelling four Britons shortly afterwards.
Mr Lavrov told a news briefing: "Britain has embarked on a programme of systematic deterioration of our bilateral relations, expelled Russian diplomats, ceased all co-operative contact with the FSB (Russian state security service), meaning any and all counter-terrorism co-operation."
Mr Lavrov said the offices "are in violation of an international convention on consular relations".
The Foreign Office has said Britain still wants to work with Russia on issues of common interest.
However, it warned the Kremlin that if it carried out its threat against the British Council it would constitute a "serious attack" against a "legitimate cultural agent" of the UK government.
A spokesman said: "It would show a disregard for the rule of law. It would penalise the thousands of Russian citizens who benefit from the council's activities.
"And it would only damage Russia's reputation around the world."
Mr Lugovoi is the main suspect in the radiation poisoning murder of Kremlin critic Mr Litvinenko, and the Crown Prosecution Service has said it has enough evidence to charge him.
He denies any involvement.
Mr Lugovoi had tea with Mr Litvinenko at London's Millennium Mayfair Hotel on the day he fell ill in November, 2006.