David Cameron to discuss 'common enemy' on Asia trip
The prime minister is expected to offer Indonesia and Malaysia support in tackling Islamist extremists, during a trade mission to South East Asia.
It comes amid growing concern that the next branch of so-called Islamic State (IS) could emerge in the region.
David Cameron said "brutal terrorists" would only be defeated if countries united against their "common enemy".
Mr Cameron is to raise the issue in meetings with the leaders of both countries during the four-day trip.
He is heading to Indonesia on the first stop of his tour, which is primarily intended to boost trade with Britain.
But Mr Cameron will also use his visit to discuss the threat from Islamist extremism with his counterparts, President Joko Widodo of Indonesia, and later Prime Minister Najib Razak of Malaysia.
'Help each other'
The UK government estimates about 500 people from Indonesia and about 200 from Malaysia have joined IS in Iraq and Syria.
The prime minister is said to be "keen to explore" whether the UK can offer more practical counter-terrorism support to both countries, such as disrupting foreign fighters, investigating potential terror plots and improving aviation security.
He is also planning to learn from their work in tackling the extremist ideology and encouraging tolerance, to explore whether the UK can learn from their approach.
Speaking ahead of his departure for Indonesia, Mr Cameron said IS was "one of the biggest threats our world has faced".
"All of us face a threat from foreign fighters and from increasing radicalisation within our countries and it's right that we look at what help we can provide to one another," he said.
Separately, it is understood the UK government has had discussions about its role in tackling IS in Libya.
There is no suggestion of any air strikes but it is thought the UK has considered what help it could offer in combating IS's presence if a stable Libyan government was formed.