David Cameron has said ITV1 presenter Phillip Schofield was wrong to hand him a list of alleged paedophiles during a live interview.
The prime minister said it was not the "right approach" and unproven claims "scrubbed off the internet" should not be bandied about in public.
Conservative and Labour politicians have criticised the show, calling its actions "irresponsible and amateurish".
TV regulator Ofcom said it had received complaints about the programme.
As the fallout from recent abuse allegations continued, Conservative peer Lord McAlpine said attempts to link him to alleged historical child abuse were "wholly false and seriously defamatory".
The ex-party treasurer released a statement after Steven Messham, one of hundreds of victims of sexual abuse at children's care homes in Wales over two decades, told the BBC's Newsnight programme a week ago that he had been abused by an unnamed senior Tory politician from the Thatcher era.
Lord McAlpine's solicitor said there was "absolutely no truth" in claims which have been circulating on the internet since the Newsnight programme that he was the politician concerned.
He said the peer was considering legal action against anyone linking him by name and implication to abuse allegations.
In Thursday's This Morning interview, Mr Cameron was being quizzed about historical claims of a paedophile ring linked to No 10 when he was unexpectedly handed a list of names by Mr Schofield, which the presenter said had been mentioned online as paedophiles.
Mr Cameron, who did not look at the list, said he was "worried" that speculation about unproven allegations could lead to a "witch-hunt particularly against people who are gay" and advised anyone with evidence of abuse should go to the police.
After the show, Mr Schofield was forced to apologise amid suggestions that the names on the card could be seen by viewers because of a "misjudged camera angle".
The TV presenter insisted he had not been accusing anyone of anything and "it is essential that it is understood that I would never be part of any kind of witch-hunt".
Asked about the exchange on Friday during a visit to Cumbria, Mr Cameron said it was "not sensible nor right to hand over a piece of paper with a few names you have just quickly scrubbed off the internet.
"Effectively you are casting aspersions about lots of people without any evidence...I don't think it was the right approach and I am sure that ITV agree with that.
"I don't want to get into a great shouting match with anybody but I don't think it is the right way to approach this extremely serious matter."
In other reaction, Mayor of London Boris Johnson said "it was a pretty rum piece of journalism" and "a very curious thing for the producers to allow to happen".
Speaking on BBC London 94.9, he said the presenter had produced a list "without any real substantiation or proper journalistic efforts to get to the bottom of whatever allegations were made about the individuals who might have been named on that bit of paper."
Mr Cameron, a former senior executive with ITV company Carlton, had behaved in "a very dignified way and dealt with it very calmly", Mr Johnson added.
Policing Minister Damian Green told BBC One's Question Time Mr Schofield's intervention was a "pretty tasteless and silly stunt".
Shadow business secretary Chuka Umunna, for Labour, told the same programme: "I think what Phillip Schofield did was foolish, stupid and grossly irresponsible. And frankly, rather amateur. It's not what you expect of serious broadcast journalism."
Conservative MP Rob Wilson has reported the programme to broadcasting regulator Ofcom, urging it to investigate whether ITV1 had breached its duty to give individuals a chance to respond before subjecting them to serious allegations on screen.
The prime minister has announced separate inquiries into alleged abuse at Welsh care homes in the 1970s and 1980s and the police investigation at the time, as well as whether the terms of an independent inquiry into the allegations in the late 1990s was too narrow.
Gay rights campaigners have criticised Mr Cameron's use of language during the interview.
"There is no reason why he should link the current scandals with gay people or warn of an anti-gay witch-hunt," long-standing campaigner Peter Tatchell said.
Mr Cameron told BBC Radio Cumbria the point he was making was there were a "lot of fingers being pointed and aspersions being cast" on the internet and social media, some of which were against people "just because they happen to be gay".
"There is a danger there and that is the point I was trying to highlight," he added.
A string of official inquiries has been launched into child abuse since allegations about the activities of the late BBC television presenter Jimmy Savile surfaced earlier this month.