David Cameron pledged to help America "destroy" self-styled Islamic State (IS) extremists in Syria as he gave his clearest signal yet that UK forces could be asked to join air strikes.

The Prime Minister said he wanted Britain to "step up and do more" if he could secure the approval of Parliament as he prepared to issue a stark warning to home-grown would-be jihadists that IS wanted them as "cannon fodder".

He will use a speech tomorrow to set out what aides said would be "significant" elements of the Government's strategy to combat the threat from fundamentalist terrorism for the next five years.

The decision to invite Labour's interim leader Harriet Harman to a National Security Council briefing on the threat last week was seen as a further step to prepare the ground for a possible parliamentary vote to extend air strikes in the autumn.

But ministers will also be forced to explain why RAF pilots were allowed to take part in bombing raids over Syria despite MPs having voted against Britain carrying out strikes in the country.

Downing Street has confirmed that Mr Cameron was aware of the missions flown by a small number of aircrew embedded with US and Canadian forces despite Parliament only authorising attacks on IS targets in neighbouring Iraq.

Asked directly in an interview for US television channel NBC if he planned to join the US-led air raids within Syria, he said: "Look, we know that we have to defeat Isil, we have to destroy this caliphate, whether it is in Iraq or in Syria.

"That is a key part of defeating this terrorist scourge that we face.

"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 it no doubt, we're committed to working with you to destroy the caliphate in both countries," he told the Meet The Press programme to be broadcast today.

In his speech, Mr Cameron will renew his focus on "shared values" and deliver an appeal to all faiths to "support the British way of life".

He will dismiss complaints that new duties on schools to prevent radicalisation amount to spying on Muslim pupils as "paranoia in the extreme" and part of the "ludicrous conspiracy theories" of plots against Islam.

And he will focus his message on convincing those tempted to travel to Syria not to buy into the supposed "glamour" of fighting for IS in the region.

Police and security services believe at least 700 extremists have travelled to fight alongside the self-styled IS and other fundamentalist groups, with around half thought to have returned to the UK.

A growing number of women and girls - 43 in the last year alone - are thought to have gone to the war-torn nation, suggesting families are fleeing there at the rate of one a week.

Most recently police confirmed they were investigating the disappearance of a family of 12 from Luton including four women and three children.

Mr Cameron, who pledged a "full spectrum" response after 30 British tourists were killed by an IS gunman in Tunisia, last month pinned some blame for UK citizens being radicalised on sections of society who "quietly condoned" extremist views.

Every aspect of that ideology has to be taken "to pieces", he will say, according to extracts released in advance.

"The cultish world view, the conspiracy theories, and yes, the so-called glamorous parts of it too," he says.

In a direct appeal to young people tempted to join IS, also known as Isil, he will say: "You won't be some valued member of a movement. You are cannon fodder for them. They will use you.

"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. That is the sick and brutal reality of Isil.

"We must de-glamorise the extremist cause, especially Isil. This isn't a pioneering movement, it is vicious, brutal, fundamentally abhorrent."

Mr Cameron will call on all parts of society to "challenge the ludicrous conspiracy theories of the extremists".

"The world is not conspiring against Islam; the security services aren't behind terrorist attacks; our new Prevent duty for schools is not about criminalising or spying on Muslim children.

"This is paranoia in the extreme.

"In fact that duty will empower parents and teachers to protect children from all forms of extremism - whether Islamist or neo-Nazi."

Local authorities, prisons, NHS trusts and schools have been placed under a statutory duty to prevent extremist radicalisation taking place within their walls.

"We have a very clear creed in our country and we need to promote it much more confidently," he will say.

"Wherever we are from, whatever our background, whatever our religion, there are things we share together.

"We are all British. We respect democracy and the rule of law. We believe in freedom of speech, freedom of worship, equal rights regardless of race, sex, sexuality or faith.

"We believe in respecting different faiths but also expecting those faiths to support the British way of life.

"Whether you are Muslim, Hindu, Jewish, Christian or Sikh, whether you were born here or born abroad, we can all feel part of this country - and we must all now come together and stand up for our values with confidence and pride."

Of the four candidates in the running to be Labour leader by the time of any possible new vote, only Jeremy Corbyn said he would definitely oppose air strikes on Syria.

The would-be Opposition leaders were asked their views during a debate for the BBC's Sunday Politics.

Shadow health secretary Andy Burnham, the bookmakers' favourite to win the contest, said: "I won't rule it out, but we have to proceed cautiously and on the basis of the evidence.

"We haven't yet seen the Government's case. I don't want Labour to just sit on the sidelines as these terrible events are taking place, but I was one of those who urged caution over Syria in the summer of 2013 and Ed Miliband was right in my view, to press, to ask for a pause at that point."

Yvette Cooper, the shadow home secretary, said: "The big questions about any intervention in Syria: is it in line with international law; is there a clear military objective and a clear moral objective?

"Of course in Syria, the Syrian government is led by Assad, there are huge problems with that and there are huge problems about who in fact you would be backing and what the implications will be."

Liz Kendall also said she would require strict conditions to be met.

"There would have to be a clear military objective about how us joining the campaign with the US would add to what they're already doing and it would have to be part of, to be honest, a much broader and wider political strategy in the region," she said.

But Mr Corbyn - the veteran left-wing MP who has caused shockwaves in the party by picking up significant levels of support - said: "No, I would not support the bombing of Syria.

"What I would support is choking off arms supplies and finances for Isil, further support for the refugees and the development of some kind of wider peace process, and I think the good news this week of the nuclear deal in Iran provides the atmosphere in which that wider debate and wider peace process can take place. Bombing will not solve it."

Scottish National Party foreign affairs spokesman Alex Salmond accused the PM of "breathtaking arrogance".

"Just two days after revelations that UK military personnel have been involved in air strikes in Syria without the approval of Parliament, he is determined to push for further action without first providing answers to serious questions that must be addressed," he said.

"And the Prime Minister casually refers to requiring the approval of 'my parliament' - when a parliament is for the people, and the House of Commons rejected bombing in Syria two years ago.

"The case for bombing in Syria has simply not been made - and the involvement of British service personnel in bombing without the approval of Parliament clearly flouts the democratic decision taken by the House of Commons.

"The Government's policy in this matter is entirely unacceptable - effectively overseeing a bombing campaign by stealth," he said, demanding Defence Secretary Michael Fallon give full details when he makes a statement on the issue to MPs tomorrow.

Tory MP Julian Lewis, who voted against air strikes on Syria in 2013 and is now the chairman of the Commons defence select committee, said he would only be persuaded to back military intervention if Mr Cameron stopped "making this up on the hoof" and developed a "coherent strategy".

Adding a relatively small number of UK air strikes to the existing US effort would be no more than a gesture unless accompanied by a wider strategy change endorsed by military chiefs, he told BBC Radio 4's The World This Weekend.

"How I vote will depend on whether the Prime Minister, instead of making this up on the hoof as has been the case I'm afraid up until now, presents Parliament with an integrated strategy, approved jointly by the heads of the armed forces as something that could produce a decisive result."

"I suspect the Government might well get this through but the problem is not going to be solved until we have an integrated military strategy and that will be the assembly of an effective army of reliable Muslim forces from the region.

"If that cannot be put together, then the idea air strikes alone will solve this problem is for the birds."