David Cameron has backed a safe passage for Syrian president Bashar al-Assad to leave the war-torn country, if it would end the killings.
The UK's most influential Syrian human rights organisation, the Syrian Observatory, has backed the prime minister's solution to the violence, even if it means al-Assad would not face a trial for war crimes.
Asked what he would say if al-Assad said he wanted a safe exit, Cameron told Saudi-owned Al Arabiya television: "Done. Anything, anything to get that man out of the country and to have a safe transition in Syria.
"Of course, I would favour him facing the full force of international law and justice for what he's done.
"I am certainly not offering him an exit plan to Britain but if wants to leave, he could leave, that could be arranged."
Rami Abdulrahman, founder and director of the Syrian Observatory for Human Rights, an anti-Assad campaign group in London, said that giving al-Assad safe passage would be a price worth paying.
"I actually think it would be a good thing," he told The Huffington Post UK, "We want to stop the killing. Around 150 people die every day. And they will continue to die if Assad does not leave the country.
"I don't want Syria to be the new Somalia, the new Afghanistan. War has been going on in those countries since I was a child. There is no end to it. It will already cost billions to repair Aleppo, Homs, Damascus. How can we already mend the feelings between neighbours? The longer it continues, that will get worse.
"I do want to see every criminal arrested that killed anyone, killed women, children, arrested, tortured, kidnapped. I want to see them all brought to justice, including Assad. But the longer we wait to end the violence, we are destroying Syria."
The SOHR estimated 37,000 people have died in the conflict since March 2011, 9,000 from the Syria army, over 1,000 government officials and the rest civilians.
In July, Nabil Elaraby, the Arab League's secretary general, said the League would guarantee the Assad family safe passage out of Syria, and Tunisian President President Moncef Marzouki has also offered Assad asylum if it would end the conflict.
But Amnesty International'S UK Syria campaign manager Kristyan Benedict told The Huffington Post UK, Cameron should be pushing for al-Assad to face trial.
“Instead of talking about immunity deals for President Assad, David Cameron should be supporting efforts to ensure that he faces justice, ideally at the International Criminal Court at The Hague.
“After Syrian government forces have indulged in a massive campaign of indiscriminate bombings, mass round-ups and torture, there should be no question of Bashar al-Assad escaping justice with a cosy deal of this kind.
“The thousands of Syrians who have lost relatives are entitled to and deserve credible justice, and President Assad and his commanders must be held to account for their brutal actions. Cameron should use all of his influence to ensure that this happens.”
In the interview, Cameron also ruled out any possibility that the should UK arming the Syrian rebels amid accusations by the Assad regime that the Saudis and other Gulf states are doing just that.
Britain would increase its humanitarian help, he said, expressing "frustration" that the international community had not done more to prevent the deaths of up to 40,000 people.
"I am very frustrated that we can't do more. This is an appalling slaughter that is taking place in our world today - 40,000 lives lost already and you can see, on your television screens, night after night, helicopters, aeroplanes belonging to the Assad regime pounding his own country and murdering his own people.
"We must ask ourselves what more can we do: how can we help the opposition? How can we put the pressure on Assad? How can we work with partners in the region to turn this around?"
Asked about arming the rebels, he said: "We are not currently planning to do that. We are a government under international law and we obey the law.
"My fear is, firstly, that the slaughter will continue, that the loss of life will continue. That should be our number one concern.
"But there is another fear, which is that the longer this goes on, the more that it can promote and drive extremism and we'll see instability in the region as well."
Cameron has now headed to Saudi Arabia for talks with King Abdullah in Jeddah - to continue his push for trade deals and investment, including Typhoon fighter jets.
Cameron said in the interview that being part of the "global race" in terms of the arms trade, was important for jobs and the economy, but he would not compromise on our strong views about human rights, which we raise with all of these countries."
"Now when it comes to Saudi Arabia, again this is a country that's very important for our prosperity but it's also important for our security too.
"As a full G20 member, we'll both be discussing Syria, Iran, other regional issues that are vital to the future security of the United Kingdom."