Cameron also appealed to Russia and China to support a new U.N. resolution that threatens non-military sanctions and is tied to Chapter 7 of the U.N. Charter, which could eventually allow the use of force to end the conflict.
"It is time for the United Nations Security Council to Pass clear and tough messages about sanctions, I believe under Chapter 7 of the U.N., and be unambiguous about it," Cameron said.
Russia, which is a close Syrian ally, has said it will veto any Chapter 7 resolution.
In Moscow on Wednesday, Russia's Foreign Minister Sergey Lavrov pointed to Wednesday's deadly bombing in the heart of Damascus that killed the defense minister and his deputy, President Bashar Assad's powerful brother-in-law, and accused the West of inciting the Syrian opposition.
Russia is vehemently opposed to sanctions and any mention of Chapter 7 and Lavrov argued that the British text amounted to support for the rebels and would lead to more bloodshed.
"I would appeal to those who in the past have held out against tough action against Syria that what more evidence do we need of a brutal regime in Syria?," Cameron said
He made the call in Kabul, where he is meeting with the Afghan president and Pakistani prime minister to discuss the ongoing war in Afghanistan.
The British leader said it was time for Assad to "go," saying that otherwise civil war is inevitable.
"It is time for him to go, it is time for transition in this regime," Cameron said. "Clearly Britain doesn't support violence on either side, but if there isn't transition there is going to be civil war. That is the clear fact that we can all see on the ground."