David Cameron expressed hope today that Syrian president Bashar al-Assad would leave office this year.
But, in an interview with American news network CNN, the Prime Minister admitted he did not know whether that would happen.
Asked whether he expected President Assad to be gone by Christmas, he said: "I would certainly hope so, but I'm not going to make a forecast."
Mr Cameron, interviewed in the Swiss ski resort of Davos where he is attending the World Economic Forum, said the international community should be "tightening the ratchet" on the Assad regime in any way it could.
But he said no one was talking about military intervention.
"This is not the same as Libya and we shouldn't pretend that it is," he said.
"I think what we should be doing is tightening the ratchet in all the ways we can, building up and working with the Syrian opposition - yes, of course, working with the Arab League, yes of course, but I don't think anyone's talking about military action."
British diplomats are pushing the UN Security Council to back the Arab League's call for President Assad, whose regime faces international condemnation for repression and violence, to step aside.
The Security Council could vote as early as next week on a new draft resolution being drawn up by Britain and France with input from Qatar, Morocco, the United States, Germany and Portugal.
But it is unclear whether Russia - which, together with China, vetoed a European-drafted resolution in October that condemned Syria and threatened it with sanctions over its 10-month crackdown on pro-democracy demonstrators - is planning to block the latest initiative.
Foreign Office Minister Alastair Burt criticised the killing of a leading Red Crescent doctor in Syria and called for a halt to ambulances and medical services being targeted.
"I was deeply shocked by reports that Dr Abdel Razzaq Jbeiro, Secretary-General of the Syrian Arab Red Crescent and president of its Idlib branch, was shot and killed yesterday while travelling in a clearly marked vehicle," he said.
"Our thoughts are with his family, colleagues and friends at this time.
"His death is part of an unacceptable trend of ambulances and medical services being targeted in Syria.
"It is absolutely crucial that everyone respects the right of Red Crescent and Red Cross staff to carry out their duties without fear of attack and in accordance with international humanitarian principles."