user: The former UK prime minister is planning a global project to prevent extremism through education.
But he warns that too often the West can "be made to feel guilty about itself" and fails to make its case.
"We're in a situation where we have to fight back," said Mr Blair.
"The centre has become flabby and unwilling to take people on. We concede far too much. There's this idea that you're part of an elite if you think in terms of respectful tolerance towards other people. It's ridiculous," Mr Blair told the BBC.
After leaving office, Mr Blair set up a foundation which works to promote greater understanding between the world's religions and to challenge extremism and prejudice.
But he warned that moderate voices were too defensive about arguing their case and this was fuelling a culture of extremism in religion and politics.
"One of the problems with the West is that it constantly can be made to feel guilty about itself - and I'm not saying there aren't things we should feel guilty about.
"But you know, we shouldn't let people intimidate us into thinking there are certain values we shouldn't be standing up for," said Mr Blair, who was attending the Global Education and Skills Forum in Dubai last week.
"I'm a supporter of multiculturalism. But there's been a long period of time when we've allowed the concept of multiculturalism to be abused."
As an example, he said that if people were asserting the equality and fair treatment of women that they should not be made to feel "somehow we're being culturally insensitive".
"We have to be clear no one has the right to abrogate those basic human rights."
On the challenge of migration and refugees, he says that in an "era of anxiety", a lack of a coherent mainstream response has opened the door to more extreme arguments.
"You have to give a real solution and not one which is populist but false. If you don't give a solution, and you leave people with a choice between what I would call a bit of flabby liberalism and the hardline, they'll take the hardline I'm afraid."
He called for a more assertive policy of "muscular centrism".
The Tony Blair Faith Foundation is promoting the idea that all countries should include a commitment to tackle extremism and promote tolerance between different religions and beliefs.
He says there is clear evidence that education can reverse the spread of intolerance and he blames extremists for cultivating bigotry and conflict between religions.
"The truth is this extremism is being incubated in school systems, formal and informal, which are teaching children a narrow minded and often hateful view of those who are different," says Mr Blair.
"What people need to understand is that this culture of hate is taught.
"They are taught a culture of hate and they can be untaught it."
"This extremist thinking is what you have to attack, if you don't attack the ideology you'll never defeat the violence."
Mr Blair says that when people are taught to hate people in other religions "it's not surprising that a proportion of them go into violent extremism".
He says that he is talking to international leaders about this proposed Global Commitment on educating against extremism - and expects countries in the Middle East to be supportive.
"What is happening in all the turmoil, particularly since the Arab Spring, is that there is a much clearer understanding in this region of the need to fight back, and a realisation that you can't fight back unless you're putting a better idea in place than the extremists."
He argues that education against extremism and intolerance will come to be seen as an international obligation - in the way that environmental policy, such as tackling pollution, is addressed by international agreement.
But Mr Blair rejected the idea that promoting values of tolerance would be seen as a form of Western interference.
"The West has just got to get over this," he said.
"There are many other people in the region who do not regard the notion of peaceful co-existence as a Western value, they see it as a sensible human value, a global value."
The former prime minister also warned that both the far right and far left were promoting arguments in favour of "isolationism and protectionism".
"People are very anxious and uncertain and they are turning to the demagogic populism of left and right."

Sum: Tony Blair has warned against "flabby liberalism" and says there needs to be a tougher centre ground approach to issues such as tackling extremism and responding to the refugee crisis.


One was killed at the base and two others died later in hospital.
They were in vehicles approaching the gate of a military training centre at al-Jafr air base when they came under small-arms fire, the official added.
An earlier statement from the Jordanian military said the car they were in failed to stop at the gate and was fired upon by security forces.
"A total of three US service members died today in the incident in Jordan," the official said.
"Initial reports were that one was killed, two injured. The two injured service members were transported to a hospital in Amman, where they died."
The Pentagon and the White House said they would work with Jordan to determine exactly what had happened.
White House spokesman Josh Earnest said the US personnel were part of an "ongoing" training mission.
"The United States is interested in getting to the bottom of what occurred," he said.
AFP news agency quoted a US defence official as saying it was a "green on blue" incident, a military term for when friendly forces attack US personnel.
"But we can't say for the moment if it was a deliberate" act to kill US personnel or "some kind of misunderstanding," the official told the news agency.
The incident happened around midday local time (10:00 GMT).
Jordan is a close ally of the US and a member of the US-led coalition fighting the so-called Islamic State (IS) group in Syria and Iraq.
US forces have trained a small group of Syrian rebels in Jordan as well as Iraqi and Palestinian security forces.
Last November, a Jordanian police captain opened fire at a police training centre near the capital Amman, killing two Americans, a South African and two Jordanians.
The Jordanian government subsequently said the police captain had been a troubled individual but security sources said he was an IS supporter.

Sum: Three US military trainers have been shot dead in an exchange of fire at an air base in Jordan, a US official says.


Cardiff Blues, Newport Gwent Dragons, Ospreys and Scarlets will form a fourth group to play a round-robin qualifier at Cardiff Arms Park on 26 July.
The top two regions will qualify for the Series Final at the Twickenham Stoop on 8 August.
"The regions have never played each other in a Sevens tournament before," said Mark Davies, the acting chief executive of Regional Rugby Wales.
We know for sure that Anglo-Welsh rugby contests ignite plenty of excitement and passion
"So there is a lot of pride at stake, as well as the opportunity of a place in the Series Final and the chance to be part of... the World Club Sevens at Twickenham in August."
The winner of the Premiership Rugby Sevens Series will go on to play in the World Club Sevens on 16 and 17 August at Twickenham.
The other three pools contain the 12 Aviva Premiership clubs, split along geographical lines.
Kingsholm hosts Gloucester, Bath, Exeter Chiefs, and London Irish in Group B, which takes place on 31 July.
Twenty four hours later Group C features Northampton Saints, Harlequins, London Wasps and Saracens at Franklin's Gardens.
Completing the group stages on 2 August at Kingston Park, Newcastle, Leicester Tigers, Sale Sharks and Worcester Warriors will battle it out in Group D.
Davies added: "Having announced our exciting three-year sponsorship agreement with BT Sport this week as well, it shows we have a positive partnership that will go forward between BT Sport and our four Welsh regions.
"We know for sure that Anglo-Welsh rugby contests ignite plenty of excitement and passion amongst our supporters and we hope our involvement will add a real edge to the event."
Gloucester are the defending champions, having won the Premiership Rugby Sevens by beating Leicester in the 2013 final.

Sum:

assistant: The four Welsh regions will compete in the Premiership Rugby Sevens Series.