David Cameron has condemned Ken Livingstone as an "ageing far left politician" for suggesting that there were no downsides to multiculturalism.
The Conservative leader said the London mayor's criticism of Trevor Phillips, the chairman of the Commission for Racial Equality (CRE), was proof that his views on race were "completely out of date".
Mr Phillips has raised doubts about the benefits of multiculturalism as a way of dealing with Britain's different communities, prompting Mr Livingstone to say he should join the BNP. Earlier this week the mayor boycotted a CRE-organised conference on race.
But in a speech to the ethic media conference yesterday, Mr Cameron said: "Insulting Trevor by saying he should join the BNP isn't a serious contribution to debate.
"It's a discreditable attempt by an ageing far left politician to hang on to a narrative about race that is completely out of date, rather than seeing people from ethnic minorities as full and equal citizens who would rather build a better life for themselves and their families than man the barricades at the behest of middle-class white fantasists.
"Ken's problem is that the critique of multiculturalism is coming from a growing number of intelligent and thoughtful young people - who are themselves from ethnic minority backgrounds."
The Tory leader said that allowing people to live in separate communities and giving them separate public recognition could increase feelings of "tribalism" between religious and ethnic groups.
"It is a climate that promotes racism rather than defeats it," he said, adding: "I believe that it's time to discard the failed policies of the past. We need to bring people together - and bring our society together."
However, Mr Livingstone hit back saying: "Every member of an ethnic minority, of any income, class or creed, now knows that they are expected by [Mr Cameron] and his colleagues to abandon their cultural identity to be really considered British citizens."
He said the Tory leader's views were "simply a softer version of the 'Tebbit test'", referring to Norman Tebbit's 1990 declaration that ethnic minorities were not really British until they supported British sports teams rather than those of their country of origin.
The mayor added: "Economically Mr Cameron's attack on multiculturalism would threaten the international character of London that gives it an advantage over its competitors - thereby undermining the prosperity of the city."
Mr Cameron admitted the Tories had not done enough to promote diversity in their own party, saying that in the past, they had assumed that by exercising a meritocracy, the situation would resolve itself.
But now, he said, more positive action needed to be taken, and the Tory leader announced a new drive to improve the representation of black and ethnic minority (BME) communities in the party.
A new monitoring system would be introduced to assess progress in recruiting more BME parliamentary and council candidates. He also unveiled a new bursary for 20 internships a year with the party in parliament or head office, for BME people.
A roadshow will also be launched with Operation Black Vote to help increase participation of BME communities and recruit more people to represent the Tories.
"The fact is that it's not enough just to open the door to ethnic minorities. If people look in and see an all-white room they are less likely to hang around. An unlocked door is not the same as a genuine invitation to come in," Mr Cameron said.
"That's why the Conservative party needs positive action if we are to represent Britain as it is."