Russia has been the staunchest backer of Assad and his military crackdown against militants and protesters in Syria, including supplying arms to the Syrian government.
But Cameron said Putin had shifted his view of the Syrian leader.
"There remain differences over sequencing and the shape of how the transition takes place but it is welcome that President Putin has been explicit that he does not want Assad remaining in charge in Syria," Cameron told reporters.
"What we need next is an agreement on a transitional leadership which can move Syria to a democratic future that protects the rights of all its communities."
Cameron said he had discussed the issue at the G20 summit with President Barack Obama, Putin, German Chancellor Angela Merkel, French President Francois Hollande and Turkish Prime Minister Recep Tayyip Erdoğan.