The Prime Minister said he wanted Britain to "step up and do more" but added that he would need the approval of Parliament to do so.
MPs voted against proposed military action in Syria two years ago.
Islamic State, also known as Isil or Isis, has forced tens of thousands of Christians to flee their homes as it advances over large parts of Iraq and Syria.
Christians have been told to pay a tax, leave or face death in areas they have lived in for a thousand years.
In an interview for US television channel NBC Mr Cameron pledged to help America "destroy" the Islamist extremists in Syria.
"Look, we know that we have to defeat Isil, we have to destroy this caliphate, whether it is in Iraq or in Syria," he said.
"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,"
The prime minister 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.
He will appeal to Christians to join with other faiths to "support the British way of life" using "shared values".
He will say complaints about spying to prevent terror attacks are "paranoia in the extreme" and part of the "ludicrous conspiracy theories" of plots against Islam.
In a direct appeal to young people tempted to join IS 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."
He'll add: "We have a very clear creed in our country and we need to promote it much more confidently.
"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."