The militant group has persecuted tens of thousands of Christians and other religious minorities in the country.
The group has forced every Christian to leave the northern city of Mosul after it overtook the area.
Mr Blair said airstrikes alone are not enough to defeat IS and that sending in combat soldiers should not be ruled out.
The former PM did acknowledge there was "no appetite" for soldiers to be sent back to Iraq, but warned it could be the only way to destroy the group.
"You cannot uproot this extremism unless you go to where it originates from and fight it," he said.
In an essay on his Faith Foundation's website he added: "There can be an abundance of diplomacy, all necessary relief of humanitarian suffering, every conceivable statement of condemnation which we can muster, but unless they're accompanied by physical combat, we will mitigate the problem but not overcome it."
The UK has so far declined to involved itself in US-led airstrikes and has instead delivered aid to the country by air.
But Mr Blair said: "Air power is a major component of this, to be sure, especially with the new weapons available to us. But – and this is the hard truth – air power alone will not suffice. They can be hemmed in, harried and to a degree contained by air power. But they can't be defeated by it.
"If possible, others closer to the field of battle with a more immediate interest can be given the weapons and the training to carry the fight; and in some, perhaps many cases, that will work. It may work in the case of Isis.
"There is real evidence that now countries in the Middle East are prepared to shoulder responsibility and I accept fully there is no appetite for ground engagement in the West.
"But we should not rule it out in the future if it is absolutely necessary.
"Provided that there is the consent of the population directly threatened and with the broadest achievable alliance...we have, on occasions, to play our part."