In a speech at Downing Street, Mr Blair said that tolerance was "what makes Britain, Britain" and warned "we must be ready to defend this attitude".
The prime minister said: "So conform to it; or don't come here. We don't want the hate-mongers, whatever their race, religion or creed."
He also defended multiculturalism, saying it should be celebrated.
The lecture comes a year after Mr Blair said he never quite knew what people meant by multiculturalism.
The right to be different. The duty to integrate. That is what being British means
Mr Blair said: "It is not that we need to dispense with multicultural Britain.
"On the contrary, we should continue celebrating it."
Conservative spokesman for community cohesion Dominic Grieve said the speech was a "remarkable turnaround".
"Many of the problems in relation to the issues he addresses are at least in part the consequence of a philosophy of divisive multiculturalism and political correctness that has been actively promoted by the Labour Party over many years at both national and local government levels."
Duty to integrate
In the speech, Mr Blair also announced a crackdown on funding for religious and racial groups, saying in the future they would have to prove they aimed to promote community integration.
It was important to demonstrate what integration meant, Mr Blair said.
"The right to be in a multi-cultural society was always implicitly balanced by a duty to integrate, to be part of Britain, to be British and Asian, British and black, British and white."
The suicide bombings in London on July 7 last year had thrown the whole concept of a multicultural Britain "into sharp relief", the prime minister said.
The prime minister put the speech in the context of Muslim extremism, associated with "a minority of our Muslim community".
He said there was optimism that people could be integrated despite different cultures.
And he said the Equal Opportunities Commission would be looking at concerns About women's status inside Muslim communities.
A spokesman for the Muslim Association of Britain said Mr Blair's speech was "concerning and alarming".
He said Mr Blair should be "investing in our society" to help the deprived, rather than investing "millions and billions in illegal occupations" which had "not helped to promote multiculturalism in this country".
"Rather than standing up and lecturing us, it's time he puts his money where his mouth is," he said.
The prime minister said: "So conform to it; or don't come here. We don't want the hate-mongers, whatever their race, religion or creed."
He also defended multiculturalism, saying it should be celebrated.
The lecture comes a year after Mr Blair said he never quite knew what people meant by multiculturalism.
The right to be different. The duty to integrate. That is what being British means
Mr Blair said: "It is not that we need to dispense with multicultural Britain.
"On the contrary, we should continue celebrating it."
Conservative spokesman for community cohesion Dominic Grieve said the speech was a "remarkable turnaround".
"Many of the problems in relation to the issues he addresses are at least in part the consequence of a philosophy of divisive multiculturalism and political correctness that has been actively promoted by the Labour Party over many years at both national and local government levels."
Duty to integrate
In the speech, Mr Blair also announced a crackdown on funding for religious and racial groups, saying in the future they would have to prove they aimed to promote community integration.
It was important to demonstrate what integration meant, Mr Blair said.
"The right to be in a multi-cultural society was always implicitly balanced by a duty to integrate, to be part of Britain, to be British and Asian, British and black, British and white."
The suicide bombings in London on July 7 last year had thrown the whole concept of a multicultural Britain "into sharp relief", the prime minister said.
The prime minister put the speech in the context of Muslim extremism, associated with "a minority of our Muslim community".
He said there was optimism that people could be integrated despite different cultures.
And he said the Equal Opportunities Commission would be looking at concerns About women's status inside Muslim communities.
A spokesman for the Muslim Association of Britain said Mr Blair's speech was "concerning and alarming".
He said Mr Blair should be "investing in our society" to help the deprived, rather than investing "millions and billions in illegal occupations" which had "not helped to promote multiculturalism in this country".
"Rather than standing up and lecturing us, it's time he puts his money where his mouth is," he said.
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