Britain's government should not shy away from talking to Russia about peace in Syria, though relations with Moscow are strained, Prime Minister David Cameron told Al Jazeera.

A British inquiry on Thursday said that Russian President Vladimir Putin "probably" approved the assassination of ex-KGB agent Alexander Litvinenko in London, increasing tensions between Russia and the UK.

Obviously, we have real difficulties with our relationships with Russia because of what has happened. British Prime Minister David Cameron

Judge Robert Owen said it was likely the Russian leader signed off the killing of the former spy in 2006 after a long-running feud.

"There is no doubt that when it comes to Syria that we need all of the players, whether it is Saudi Arabia or Iran or Russia. Everyone needs to be involved," Cameron said in a wide-ranging interview with Al Jazeera on the sidelines of the Davos summit.

"Obviously, we have real difficulties with our relationships with Russia because of what has happened, and it is right we take the action we announced yesterday, but when it comes to Syria, difficult as it is, we have to discuss these issues with them because the crisis will only be solved when all the players recognise that it is in their interest to have a settlement," he added.

READ MORE - UK Judge: Putin 'probably' approved killing

UN-backed talks between the Syrian government and opposition are scheduled for Monday, though officials have said they might be briefly delayed.

When asked whether Britain would agree to accept more refugees as the crisis in the Mediterranean continued, Cameron said his government did not want to incentivise people to travel to the UK.

"We said we will take 20,000 refugees from the Syrian refugee camps in Jordan, Lebanon and Turkey. We don't want to provide an extra pull factor into Europe. We said we will resettle a thousand by Christmas, and we did that," Cameron said.

Watch the full interview in the video above