British Prime Minister David Cameron wants Russia and Syria to demonstrate that a Moscow-backed proposal for President Bashar al-Assad to put his chemical weapons under international control is genuine, Cameron's spokesman said on Tuesday.

"The onus is very much now on the Russian government and the Assad regime to follow up in a way that shows the initiative is a serious and genuine offer," the spokesman said, adding, many serious questions remain that need to be answered.

Cameron said on Monday that Syria should be encouraged to go along with the plan, but warned the world to make sure the idea was not a tactic to delay a US response to a suspected chemical weapons attack on 21 Aug.

On Tuesday, Cameron's spokesman said the world's response to the attack could not drag on indefinitely. "This cannot be in any way an endless process," he said, adding, "we must be very vigilant about the risk of distraction tactics."

Serious questions remain about how such a process might be organised, the spokesman said, noting that as recently as Monday - in a TV interview - Assad was not acknowledging that his government actually possessed a stock of chemical weapons.

Cameron and US President Barack Obama have discussed the issue of how Syria's chemical arms could be controlled, the spokesman added, saying he did not think a statement by US Secretary of State John Kerry on Monday about the need for Assad to hand over his chemicals weapons was "a gaffe".