World leaders remain "miles apart" over the Syria crisis, David Cameron conceded as he dismissed any prospect of any "phoney" solution that involved Bashar Assad.
The Prime Minister is at the United Nations in New York where talks between Western allies and their Russian and Iranian counterparts have failed to break the deadlock over taking on Islamic State (IS).
Speaking to CBS before joining allies at a UN meeting to discuss how to step up the fight against IS - also referred to as Isil - he said it was "the most difficult intractable problem".
"I will work with anybody to build a Syria that is free of Iraq and free of Isil," he said after talks yesterday with Iran's president Hassan Rouhani.
"We are miles apart at the moment but we need to try and build that understanding that fundamentally we will never have a secure Syria until both those things are eradicated.
"In the end, however far apart we might be whether with the Iranians or the Russians, those two countries have an influence over what happens in Syria and we need to convince them that a new Syria with a different leader wouldn't necessarily be against their interests but it would help to get rid of Isil.
"So far the problem has been that Russia and Iran have not been prepared to contemplate the end state of a Syria without Assad."
Vladimir Putin - who met face to face with US president Barack Obama for discussions last night - said it would be "an enormous mistake" not to involve the Syrian president.
He has suggested his country could join the US-led coalition campaign of air strikes against IS targets.
But the US, France and the UK are demanding assurances Assad will eventually be ousted.
"The meeting between Obama and Putin last night was important but we need much more of that to try to build some sort of shared understanding," Mr Cameron said.
He said he believed a Russian military build-up in Syria was a response to concerns Assad was "on the brink of falling", he said.
"What we have to do is convinced them that it is going to be a pretty poor investment unless there's a transition of government away from Assad.
"Because in the end, those 12 million people who have left their homes, they are not going to go back to their homes if the butcher is still in charge of the country."
He went on: "Is this the most difficult intractable problem that President Obama has faced and that I face? Yes.
"We are four years into this. So many people have died and so many have left the country but that doesn't mean you give up.
"Nor should it mean that you go for a sort of phoney solution of thinking you could team up with Assad to fight Isil, because that would be self defeating.
"You have to stick to the right path, no matter how long it takes and then persuade others."
He conceded that the failure of Western governments to properly train moderate opposition forces had left the door open to IS.
"We did do work to train moderate opposition forces but we haven't done enough, they haven't been successful enough and so they are a big enough presence."
At the meeting - which will include Mr Obama - Mr Cameron will set out plans for a £10 million UK-run counter-propaganda drive to blunt the effective use of social media by IS to spread its message.
In a bid to stem the recruitment of home-grown jihadis, the Government has also had four British citizens - two men and two women - placed under UN sanctions.
The move provoked a mocking response for one of the quartet of Syria-based militants, with a post on a Twitter account thought to belong to Sally-Anne Jones referring to "laughing out loud".
Mr Cameron is due to hold talks with the Turkish prime minister before leaving the US to travel to Jamaica to push the UK's role in building Caribbean economies.
Foreign Secretary Philip Hammond will deliver the UK's address to the UN's annual General Assembly - sparking accusations from Labour that the PM was failing to show leadership on Syria.