In his closing speech at the UN General Assembly's 69th session, British Prime Minister David Cameron argued that Syria needs an "inclusive, representative, democratic" government that can "look after the interests of all its people."
Although he said it was "not credible" that Assad should lead such a future government, he expressed readiness to look at "every practical option to find a way forward".
Cameron addressed countries both backing Assad or " have stood on the sidelines" during this speech, expressing readiness to join them in a " new political effort to secure a representative and accountable government in Damascus that can take the fight to ISIL."
"Syria needs what Iraq needs," he said. "Now I know there are some who think that we should do a deal with [President Bashar] Assad in order to defeat ISIL. But I think this view is dangerously misguided. Our enemies' enemy is not our friend. It is another enemy."
The Conservative premier stressed that making a deal with Assad's regime will not lead to a victory against Islamic State (IS) militants as its "bias and brutality" represents "one of the most powerful recruiting tools for the extremists."
Cameron warned that IS is a threat to "all of us," as well as the "greatest threat to the region."
"It is very welcome that a number of Arab countries have already taken part in the action to degrade ISIL. They have shown courage and leadership," he said.
Concerning Iran - the key regional ally of the Syrian regime - Cameron called for giving the Islamic republic a "chance to show it can be part of the solution, not part of the problem."
"Earlier today I met with President [Hassan] Rouhani. We have severe disagreements. Iran's support for terrorist organisations, its nuclear programme, its treatment of its people. All these need to change,"Cameron pointed out, adding that the world should welcome Tehran's engagement if "they are prepared to do this."
He also said Britain's military can support enormous humanitarian efforts, mentioning the help provided by the Royal Air Force to millions of people who fled IS's violent campaigns. And we should - together - do more to build the capability of the legitimate authorities fighting the extremists," Britain's top government official said.
"I don’t believe this threat of Islamist extremism will best be solved by western ground troops directly trying to pacify or reconstruct Middle Eastern or African countries. But pursuing an intelligent and comprehensive approach should include a place for our military."
A US-led coalition launched its first strikes on militant jihadists in Syria on Tuesday, mainly against the IS group - who have vowed revenge - and the Al-Qaeda affiliated Al-Nusra Front.
Members of the UK's House of Commons will hold an extraordinary session on Friday to discuss and vote on being part of the coalition.