In a speech in New York, the former prime minister said that warnings over the past week of new terrorist plots against Europe should remind people that they remain under threat.
Mr Blair said a "narrative" that Muslims were under attack from the US and its allies, who act out of support for Israel, had been allowed to take hold, aided by "websites and blogs".
A fresh confrontation is needed because it will be impossible to defeat extremism "without defeating the narrative that nurtures it", he said.
"The practitioners of extremism are small in number. The adherents of the narrative stretch far broader into parts of mainstream thinking," Mr Blair told the Washington Institute for Near East Policy.
"It is a narrative that now has vast numbers of assembled websites, blogs and organisations." Mr Blair said it was "absurd" that some people were surprised at how powerful Islamist extremist groups were, given the amount of funding they received and indoctrination they spread.
"Measure, over the years, the paucity of our counter-attack in the name of peaceful coexistence," he said. "We have been outspent, outmanoeuvred and out-strategised."
Mr Blair said a tendency to "sympathise" with extremism was not only dangerous but also disempowering for moderate Muslims, because it made people resent them as much as extremists.
He said he was "intrigued" by the fact that western leaders, including Barack Obama, the US President, felt the need to condemn Terry Jones, a pastor who threatened to burn a Koran.
"Suppose an Imam, with thirty followers, in Karachi was to burn a bible," he said. "I can barely imagine a murmur of protest. It wouldn't be necessary for the President of Pakistan to condemn it because no one here would remotely consider he supported it."
The former prime minister also called on the west to make it "crystal clear" to Iran that their acquisition of a nuclear bomb would be unacceptable to the entire "civilised world".
"Go and read the speech of Iran's President to the United Nations just days ago here in New York, and tell me that is someone you want with a nuclear bomb," he told those who disagree.
He stressed that the achievement of a peace settlement between Israel and Palestine would remove "much of the poison which the extremists use".
And he defended his decision to invade Iraq and Afghanistan, saying: "whatever you think of the original action, we enabled the people to choose their Government"
*Mr Blair last night appeared on the Late Show with David Letterman on American television. He said that satirists like Letterman had been wrong to paint George W. Bush as unintelligent. "You don't get to this position by being a fool," he said.
