(Adds quotes, details, background) LONDON, July 19 (Reuters) - U.S. Secretary of State Condoleezza Rice urged Russia on Thursday to honour Britain's request to extradite a suspect in the murder of former intelligence officer Alexander Litvinenko. "A terrible crime was committed on British soil and Britain has to find the perpetrators and bring them to justice," Rice told Sky News in Lisbon ahead of a meeting of the Quartet of Middle East negotiators. "Russia should honour the extradition request and Russia should cooperate fully." Moscow has said its laws do not allow it to extradite Russian citizens to face courts overseas, but has said that Andrei Lugovoy, a former KGB agent whom British prosecutors want to charge with Litvinenko's murder, could be tried at home. Britain this week expelled four Russian diplomats as a result of Moscow's refusal to extradite Lugovoy. Moscow on Thursday announced the retaliatory expulsion of four British diplomats. Despite the deepening diplomatic stand-off, with its echoes of the Cold War, Rice said modern-day Russia was a far cry from the former Soviet Union and said there was "nothing to be gained" from isolating the country. "Russia is a factor in the Middle East and we need to pursue those areas of cooperation," said Rice, who as a student was a specialist in Soviet affairs. "Because if you try and simply paper them over (differences) you won't deal effectively with them. But most importantly to remember that I think there is nothing to be gained by the isolation of Russia." Russia is a member of the Quartet, which also includes the United States, the European Union and the United Nations. As well as its dispute with Britain, Russia and its President Vladimir Putin have had disputes with neighbours, particularly former Soviet state Ukraine, in which Moscow has cut off Ukraine's access to supplies of power to put pressure on the country. Rice said such tactics were wrong. "We all are concerned that Russia not use its energy resources somehow as a political tool but rather engage in an open international economy in which oil and gas can fuel economic growth for everyone," she said.
