The British authorities say they are seeking the extradition of a former Russian agent to face a charge of the murder of Alexander Litvinenko in London last November.
Andrei Lugovoy has denied any involvement and said the charges against him were 'politically motivated'.
A spokesman for the Kremlin has said Russia's constitution did not allow its nationals to be extradited.
Earlier, the Crown Prosecution Service for England and Wales decided there is enough evidence to charge the Russian with the murder of the former KGB agent.
Mr Litvinenko, a critic of Russian President Vladimir Putin, was murdered in London last November.
The 43-year-old, who had been granted political asylum in Britain, died in hospital after being exposed to Polonium 210, a radioactive substance.
A warrant was today issued for the arrest of Moscow-based Andrei Lugovoy, although Britain and Russia have no extradition treaty.
The case is likely to cause further strain to relations between the two countries.
Britain's Foreign Secretary Margaret Beckett said full cooperation was being sought from the Russian authorities, but the Prosecutor General's Office in Moscow said Mr Lugovoy would not be extradited.
Ken Macdonald, Director of Public Prosecutions, said the CPS would be contacting Moscow about the case.