Bolstering the democratic elements among the Syrian opposition is vital if it is not to be taken over completely by extremists, David Cameron has warned.
The Prime Minister said that he had still not made a decision on whether to follow US President Barack Obama's lead on supplying arms to the rebels.
However he said Britain would continue to offer non-lethal support to what he called the "genuine" opposition - despite fears that elements linked to al Qaida have been seeking to acquire chemical weapons.
"Yes there are elements of the Syrian opposition that are deeply unsavoury, that are very dangerous, very extremist and I want nothing to do with them. I'd like them driven out of Syria - they're linked to al Qaida," he said in an interview with Sky News's Murnaghan programme.
"But there are elements of the Syrian opposition who want to see a free democratic, pluralistic Syria that respects the rights of minorities including Christians and we should be working with them - we are working with them.
"If we don't work with those elements of the Syrian opposition, then we can't be surprised if the only elements of the Syrian opposition that are getting, that are actually making any progress in Syria are the ones that we don't approve of.
"After all, they are trying to defend their communities against appalling attacks, including, let's be clear, chemical weapon attacks. President Assad is now guilty of the most appalling crimes against his people - 90,000 people dead and some of them through the use of appalling chemical weapons."
Mr Putin has made no secret of his opposition to the West arming the rebels. He responded to the recent lifting of the EU arms embargo by reaffirming his intention to supply the regime of President Bashar al-Assad with sophisticated anti-aircraft missiles in order to deter "hotheads" from intervening in the conflict.
The Russian president has also reacted sceptically to evidence produced by Britain, France and Russia that the regime has used chemical weapons against its own people - Mr Obama's justification for deciding now to start arming the rebels.