The former British prime minister said that tackling "a radicalized and politicized view of Islam" should be at the top of the global political agenda.
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 U.S. and Russia.
In a speech in London, he said that "whatever our other differences, we should be prepared to reach out and co-operate with the East, and in particular Russia and China," to combat Islamic extremism.
Blair's political legacy in Britain is tarnished by his decision to lead the country into the divisive invasion of Iraq in 2003.
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."
Blair argued that "on the fate of Egypt hangs the future of the region."
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."