The former British prime minister said that tackling "a radicalised and politicised view of Islam" should be at the top of the global political agenda.
He said many in the West seemed "curiously resistant" to face up to a force that "is undermining the possibility of peaceful co-existence in an era of globalisation."
Blair, Britain's prime minister between 1997 and 2007, is now Middle East envoy for the Quartet of the United Nations, the European Union, the US and Russia.
Blair's political legacy in Britain is tarnished by his decision to lead the country into the divisive invasion of Iraq in 2003.
Also Read
Blair acknowledged the invasions of Iraq and Afghanistan had undermined Western willingness to intervene in the Middle East. But he called for the West to engage with the region, saying "we have to stop treating each country on the basis of whatever seems to make for the easiest life for us at any one time."
He defended the coup that overthrew the elected Muslim Brotherhood government of Mohammed Morsi last year, saying "the Muslim Brotherhood government was not simply a bad government. It was systematically taking over the traditions and institutions of the country."
He said the protest that led to Morsi's ouster "was not an ordinary protest. It was the absolutely necessary rescue of a nation. We should support the new government and help.