Mr Cameron said his "fundamental point" was still right
David Cameron has defended his claim that government money is being used to fund schools run by an organisation "with links to extremists".
Ministers denied the Tory leader's allegation that cash came from an "anti-extremism" fund, adding that it was from a separate scheme.
But Mr Cameron told the BBC that the "fundamental point" that state money was being used was still true.
The row relates to two Muslim schools in Slough and Haringey, north London.
Mr Cameron says these were set up by "an extremist Islamist foundation" which was a "front" for Hizb ut-Tahrir, a group which campaigns for an Islamic state across the Middle East.
Hizb ut-Tahrir, which is not banned in the UK, denies links to terrorism and says it opposes violence.
At prime minister's questions on Wednesday, he claimed the schools had secured £113,000 of government money and, of this, some was from a Pathfinder scheme whose objective was to prevent violent extremism.
But the local authorities said the Pathfinder fund in question was one for helping parents find nursery places.
Schools Secretary Ed Balls said the way Mr Cameron had raised the issue in the Commons "based on a whole series of facts which are false is, I think, deeply irresponsible".
Tory aides have agreed some of the information was inaccurate.
But when questioned by the BBC, Mr Cameron said: "Look, the fundamental point is that two schools are being funded and run by an organisation with links to extremists. No-one is denying that.
"And the other fundamental point is that they did receive government money. That is another fundamental point that the government now seem to be admitting to.
"That's the problem - schools run by an extremist organisation getting government money. That's the problem. That's what I raised. That's what the government needs to answer for."
In 2005 the then prime minister Tony Blair said he would outlaw Hizb ut-Tahrir but two Home Office reviews concluded there was insufficient evidence to do so.
The Conservatives have said they will ban the organisation if they win power.
In a letter to Mr Cameron, Gordon Brown said the decision to ban a group "must be based on evidence that the group has broken the law" - and Hizb ut-Tahrir had not met that "legal test" under the Terrorism Act 2000.
In a statement Hizb ut-Tahrir accused Mr Cameron of "baseless allegations" and said it never accepted funding from government.
Spokesman Taji Mustafa said it was a political party that did not run schools, adding: "David Cameron's bare-faced lies that Hizb ut-Tahrir runs schools, receives government funding and promotes hatred and violence are another desperate attempt to boost Conservative poll ratings."