In an article Dr Fox, urges ministers to be prepared to send British military assets to the region to help any American-led attacks on fighters from the Islamic State of Iraq and al-Sham (Isis).
However, he warns that any assistance provided by the west must be as part of a political deal for a major change in the policy of the “inept” Iraqi Prime Minister, Nouri al-Maliki.
The Iraqi government has fuelled sectarian resentment by failing to embrace both Sunni and Kurdish politicians in its ranks, he says.
The Syrian civil war has drawn radicalised youths from around the world and destabilised the region.
“When young jihadists develop the habit for hating it can be hard to break,” Dr Fox warns.
“Our security forces know that many do not lack the will to kill us, merely the capability. We will have to redouble our efforts to ensure that remains the case.”
His comments follow warnings that up to 500 British born fighters have travelled to Syria and Iraq to take part in Islamist fighting.
“It is clear that the Isis must be defeated,” Dr Fox writes. “The shocking pictures of mass, summary executions and the brutality of both their methods and beliefs would be reason enough to want to stop them.
“The risks that the creation of a fanatical Islamic state, extending from Lebanon to the borders of Iran, would create merely add to the imperative.
“On one hand, there is a real possibility of creating a sectarian clash across the region, whose political and economic effects would be felt quickly round the world, not least as it would likely spark a huge rise in the oil price, with all the consequences we have come to know and fear.
“On the other, the idea of extremists waging successful jihad and then returning to their countries of origin, including the United Kingdom, should concentrate the minds of both government and citizens.”
He says it is “highly likely” that the US will be required to intervene with force to stop the Isis threat but warned that the UK “should not rule out acting where we could provide specific help”.
William Hague, the Foreign Secretary, has said there will be no role for British military in the Iraq crisis.