Most Revd Justin Welby has suggested setting up informal "back channels" with the group, similar to the secret communications with the IRA which paved the way for the Northern Ireland peace process.
However Archbishop Justin also said I.S. represented a "lethal danger to the human values on which civilised life depends" and reiterated his support for UN-backed military action.
He made the comments as part of a lecture on religiously motivated violence at Liverpool John Moores University in which he also used a series of frank behind-closed-doors conversation about sexuality, currently taking place in the Church of England, as an example of how powerful meeting people of opposing views face to face could be.
The so called "shared conversations" on gay marriage are being chaired by conflict resoloution experts and could end up costing the Church of England up to £500,000, according to one Synod member.
"To sit in the same room, in a chair across from somebody with whom you disagree profoundly, and to listen to them and to talk to them – the effect is remarkable," he said.
He went on: "We need to turn face to face with other religious leaders, other politicians, with integrity and generosity.
"And once we have faced each other and begun to break down the barriers of self-preservation, we can start to look outwards, side by side, and take action together."
He said government figures must be taught to understand religion better, so that decisions are not clouded with "poorly nuanced preconceptions and prejudices".
"Above all, as I have said, these actions need to be taken through genuine face-to-face encounter ... but for that to happen we must face each other," he said.
The Archbishop's speech comes only days after the Prime Minister set out the government's strategy to defeat the "poison" of Islamist extremism.
David Cameron pledged to tackle extremist ideology and "the failures of integration" which he said had led to hundreds of Britons joining Islamic State (IS) militants.
Church of England member Revd Canon Jonathan Ford giving his reaction to the Archbishop's commemnts:
