David Cameron has insisted he was not "singling out Muslims" in a recent speech on multiculturalism.
Mr Cameron's call for an end to "state multiculturalism" sparked debate around the world, with some accusing the UK prime minister of attacking Islam.
Explaining his words to students in Qatar, he backed a "multiracial" society but not a "super tolerant" one in which people lived separate lives.
Mr Cameron, who is touring the Middle East, also spoke up for gay rights.
In a speech on the causes of terrorism and radicalisation in Munich last month, Mr Cameron blamed "state multiculturalism" for a "weakening of our collective identity" and said it encouraged different cultures to live "separate lives, apart from each other and apart from the mainstream".
It echoed sentiments from German Chancellor Angela Merkel last October and was followed by similar comments from French President Nicolas Sarkozy last month.
But the speech prompted much comment in the UK and abroad - with some foreign commentators seeing it as an end to Britain's tradition of racial and religious tolerance, or even a direct attack on Islam.
Mr Cameron, who is on a tour of the Middle East, was quizzed about the speech as he took questions from students at Qatar University.
One student asked him whether he was "singling out" Muslims and causing division and asked where the British "spirit of tolerance" was.
Mr Cameron said his speech had to be read in full: "What I'm attacking is not the idea of a multi-racial society. Britain has an incredibly successful multi-racial society, we have people from all over the world, people from all different religions, all different colours, all different creeds living in our country."
He said he had been attacking "state multiculturalism, which was the doctrine that we had in our country for too long that you kept people separate" - where different immigrant groups would live together, speak their own language, go to their own schools and not integrate.
"It was that argument, that we should be 'super tolerant' and say everyone exists separately rather than trying to build a house together - that is the idea I was attacking.
"We should be clearer that when people come to our country, we should welcome them, we should not force people to assimilate in every single way but we should ask people to integrate, to become part of society."
He added: "Was I singling out Muslims? No."
He said he was making a distinction between Islam "one of the world's great religions" which was "peacefully observed by over a billion people" and a "very politicised extreme form of Islamism" which promoted conflict between Muslims and the rest of the world.
He also argued that the West had to "create societies that people want to integrate into.. if we leave British Muslims outside that society they may be attracted by this political extremism". And he said the West had to offer the Middle East the idea of an open, more democratic society.
At a press conference with the Qatari prime minister Sheikh Hamad bin Jassim, Mr Cameron also suggested holding the World Cup in Qatar could help change attitudes towards homosexuality.
Qatar, where homosexuality is illegal, will become the first Middle East country host the World Cup in 2022.
In December Fifa President Sepp Blatter provoked controversy when he suggested, apparently jokingly, that gay football fans going to the event should "refrain from sexual activity". He later apologised for any offence.
Questioned about the issue on his visit to Qatar, Mr Cameron said: "Football is for everybody - no one should be excluded on the basis of their race or religion or sexuality.
"It is absolutely vital that is the case. I am sure that will be the case when the World Cup comes here."
He said football could be "a great engine for social change and a change of attitudes" and had helped drive racism out of the stands in the UK.
"Just as that has happened, so too, we need to make sure that there is no place for homophobia in football."
The Qatari PM said that he was glad the question had been directed at Mr Cameron as that was "less embarrassing to me".