An inquiry into the death of Russian spy Alexander Litvinenko has heard that he told British police that Russian President Vladimir Putin had ordered his death.

Mr Litvinenko, who died three weeks after drinking tea poisoned with a rare radioactive isotope, was a critic of the Kremlin.

British authorities believe he was poisoned with green tea laced with polonium-210 at a hotel in London in 2006, during a meeting with two Russians, Andrei Lugovoy and Dmitry Kovtun.

In opening submissions, the lawyer to the inquiry, Robin Tam, repeated earlier assertions that secret British government evidence provided a "prima facie" case of Russian culpability.

The public inquiry heard that Mr Litvinenko had made the accusation himself from his hospital bed shortly before his death.

"I have no doubt whatsoever this was done by the Russian secret service," Mr Litvinenko told British detectives.

"Having knowledge of the system I know that the order about such a killing of a citizen of another country on its territory, especially if it's something to with Great Britain, could have been given by only one person.

"That person is the President of the Russian Federation, Vladimir Putin," he said. 

The Kremlin has always denied any involvement in the death as have the main suspects.

Russia has rejected British attempts to extradite the two men, but inquiry chairman Robert Owen said they had been invited to give evidence by video link from Russia.

"The issues to which Mr Litvinenko's death gave rise are of the utmost gravity and have attracted worldwide interest and concern," Mr Owen told the inquiry at London's High Court.

The controversy generated by the killing chilled Anglo-Russian relations to a post-Cold War low.

As ties improved, Britain rejected holding an inquiry in 2013, but with relations subsequently soured by the Ukraine crisis, the British government changed its mind last July.

Inquiry lawyer Tam said the evidence showed there had been a previous attempt to poison Mr Litvinenko during meetings he had the month before with Lugovoy and Kovtun.

Tests had shown traces of polonium at offices, hotels and planes used by the two Russians, he said.

Mr Litvinenko, who fled Russia exactly six years before he was fatally poisoned, had become a stringent critic of President Putin and the FSB security agency successor to the KGB.