Britain is committed to working with the US to destroy the “caliphate” set up by Islamic State militants in Iraq and Syria, the prime minister has said.
MPs voted against proposed military action in Syria two years ago.
Lord Richards, former chief of defence staff, called for a new strategy to defeat IS, saying he suspected ground troops would be deployed in the future.
Mr Cameron is due to use a speech on Monday to warn young Britons tempted to join IS fighters they will end up as little more than “cannon fodder”.
“If you are a boy, they will brainwash you, strap bombs to your body and blow you up. If you are a girl, they will enslave and abuse you,” he will say.
Speaking about the UK’s possible role in fighting the group, Mr Cameron told NBC: “I want Britain to do more. I’ll always have to take my parliament with me.
“We’re talking and discussing at the moment, including with the opposition parties in Britain, what more we can do. But be in no doubt, we’re committed to working with you to destroy the caliphate in both countries.”
Speaking on the BBC’s Andrew Marr Show, Lord Richards said military leaders need to “look again” at the strategy to defeat IS, saying the current plan “won’t work in the time I think we have available”.
He said the current strategy – of training and equipping local fighters to do the “hard work” – could prove successful, but warned the “scale of effort” going into it was “woefully insufficient”.
“If you really want to get rid of them we effectively need to get on a war footing,” he told the programme, saying he suspected UK and US troops would, in the future, have to join ground efforts against IS.
But new Liberal Democrat leader Tim Farron said he was “deeply worried” by the tone of Mr Cameron’s comments, saying he was playing to the “ISIS narrative”.
“What we ought to be doing is to get behind the Muslim communities in that region and supporting them through diplomatic means,” he told Sky News.
Last week, Labour’s interim leader Harriet Harman was invited to a National Security Council briefing on the threat in Syria – which was seen as a further sign of a possible parliamentary vote to extend air strikes in the autumn.
But Labour and the Lib Dems have called for an explanation in Parliament after it emerged that RAF pilots had taken part in bombing raids over Syria despite MPs having approved action against IS only in Iraq.
Downing Street has confirmed that Mr Cameron was aware of the Syria missions flown by UK aircrew embedded with US and Canadian forces.
And Defence Secretary Michael Fallon, who encouraged MPs to consider military action in Syria earlier this month, has defended the UK involvement saying it is “standard operating practice”.