The former Prime Minister won the endorsement of EDL leader Tommy Robinson for his article urging politicians to "be honest" about the threat.
Critics pointed out that the Blair-led invasion of Iraq is seen by many as the reason many young Muslims have become radicalised.
Blair described the ideology behind the murder of Drummer Rigby as "profound and dangerous".
He said "the seeds of future fanaticism and terror" were being sown, so children in the UK and abroad must be educated about the place of religion in society.
In the Mail on Sunday column, Blair wrote: "There is not a problem with Muslims in general. Most in Britain will be horrified at Lee Rigby's murder.
"But there is a problem within Islam - from the adherents of an ideology that is a strain within Islam. And we have to put it on the table and be honest about it."
He said "at the extreme end of the spectrum are terrorists" but "by and large we don't admit it".
Blair wrote about how a significant minority of Islamists with an "exclusivist and reactionary world view" were loud and well organised.
He went on: "The seeds of future fanaticism and terror, possibly even major conflict, are being sown. We have to help sow seeds of reconciliation and peace. But clearing the ground for peace is not always peaceful."
He said "we should never forget" that the conflicts in Iraq and Afghanistan were long and hard because "we allowed failed states to come into being".
He also warned that achieving security in troubled nations was not enough to tackle the problem of extremism.
"We resisted revolutionary communism by being resolute on security; but we defeated it by a better idea: Freedom.
"We can do the same with this. The better idea is a modern view of religion and its place in society and politics. There has to be respect and equality between people of different faiths. Religion must have a voice in the political system but not govern it.
"We have to start with how to educate children about faith, here and abroad," he said.
Blair added: "Now, more than ever, we have to be strong and we have to be strategic."Suggest a correction