The United States is backing Britain's demand for Russia to hand over the prime suspect in the murder of Alexander Litvinenko for trial.
Yesterday, Russian President Vladimir Putin expelled four British diplomats from the Moscow embassy in a tit-for-tat retaliation in the row over Mr Litvinenko's death.
Russia is refusing to comply with Britain's request for the extradition of former KGB agent Andrei Lugovoy.
Mr Lugovoy yesterday claimed British agents wanted to use his private security company as a cover for spying and gathering dirt on Mr Putin.
US Secretary of State Condoleezza Rice said: "A terrible crime was committed on British soil and Britain has to find the perpetrators and bring them to justice. Russia should honour the extradition request and Russia should co-operate fully, because it is not in anybody's interest that we can have a crime committed of this kind and nothing is done about it.
"I would hope, and we are encouraging, that there should be full co-operation from Russia, and indeed extradition."
Yesterday's expulsions were widely seen as a sign that Mr Putin did not want to escalate the dispute, however, as they exactly mirrored Foreign Secretary David Miliband's announcement on Monday that four diplomats were being sent home from Russia's London embassy.
The Russian president made clear he did not regard the situation as a return to Cold War enmity, describing it only as a "mini-crisis" that could be overcome.