Britain would be prepared to allow Syria's president, Bashar al-Assad, to be given safe passage to a third country, it has emerged, as fears rise that a prolonged conflict will fuel extremism.

In remarks released as David Cameron arrived in Saudi Arabia – a country that is a strong supporter of the Syrian opposition – the prime minister said he would agree to "anything" to see Assad removed from power.

Britain is usually wary of allowing leaders accused of war crimes to be granted a safe haven on the grounds that they should face international justice. But Cameron, who indicated that Britain would not facilitate Assad's passage out of Syria, said he was determined to see Assad removed. There are fears that extremism will flourish if the conflict continues.

Asked on al-Arabiya television what he would say if Assad demanded safe passage, the prime minister said: "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."

The Syrian conflict was expected to dominate the agenda on Tuesday when Cameron meets King Abdullah of Saudi Arabia in Jeddah. The Saudis have been leading supporters of the rebels seeking to overthrow Assad.

The prime minister, who spoke of "appalling slaughter" in Syria, reached out to his Saudi hosts by saying Britain was keen to support the opposition. For the moment this will stop short of offering arms.

Cameron said: "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 whether Britain would help arm 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."

The prime minister said extremism could flourish if the conflict were allowed to continue. He said: "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, who will discuss Saudi Arabia's fears about the Iranian nuclear programme, will use the visit to press the king to place a second order for the Eurofighter Typhoon jets. Saudi Arabia has already acquired 72 of the aircraft.

Britain is hoping to secure sales of an extra 100 Eurofighters across the Gulf. This would be worth £6bn to British firms.

At the end of Cameron's visit to the United Arab Emirates, a joint communique issued by the two countries said that the UAE and Britain planned to establish a defence and industrial partnership involving close co-operation around the Typhoon.

The statement said the defence alliance would also collaborate on "a number of new technologies", but did not elaborate.

Cameron promoted the Typhoon to Emirati ministers during his visit and his office and BAE officials have said the Emiratis have shown interest in ordering up to 60 of the aircraft. The two countries have also been discussing how to develop a "strategic air defence relationship".

Tuesday's communique said the UAE and Britain would increase their joint military exercises and training. It pledged easier travel between the two countries, but gave no details.

Cameron made an unapologetic defence of his three-day trip to the Gulf amid criticism from Amnesty International of a "deeply disturbing tradeoff" between trade and the promotion of rights. He said: "When it comes to Saudi Arabia … 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."

Downing Street is likely to point out that François Hollande, the French president, made an identical trip to Jeddah two days ago. France aggressively promotes its arms trade.