Mr Quick said the newspaper story had forced him to move his family
David Cameron is seeking a retraction from one of Britain's most senior policemen after he claimed the Tories had mobilised the press against him.
The head of Britain's anti-terror squad Bob Quick says they tried to undermine his inquiry into Home Office leaks, which led to MP Damian Green's arrest.
Mr Quick later withdrew suggestions they had behaved in a "corrupt" way.
Mr Cameron rejected Mr Quick's claims and said he "has to withdraw what is a completely baseless allegation".
The Conservative Party leader added, on London's LBC radio: "I am sure he will want to do that because in life, if you make a mistake, the best thing to do is correct it as quickly as you can."
Mr Quick said on Sunday he had been forced to move his family after an article published in the Mail on Sunday put them at risk.
"The Tory machinery and their press friends are mobilised against this investigation," the Metropolitan Police assistant commissioner told reporters.
"I think it is a very spiteful act, possibly to intimidate me away from investigating Mr Green, and I feel it has put my family at risk."
Mr Quick said he would be consulting his solicitor about further possible action.
Mr Cameron said: "I can absolutely guarantee that the Conservative Party had nothing to with the publication of this story."
Former shadow home secretary David Davis said Mr Quick's allegations were "completely baseless" and told BBC Radio 4's Today programme: "If there is any evidence he should name who he thinks is responsible or withdraw his allegations."
Mr Davis said he believed the police inquiry into the Damian Green affair was "not going anywhere" but if it did carry on, a different officer should be put in charge.
Mr Cameron told LBC he was "perfectly happy" to work with Mr Quick on a professional basis, but added that he thought the investigation into Mr Green was "misconceived and the sooner it comes to an end the better, and I suspect it will fairly shortly".
The arrest of Mr Green and the search of his home and offices earlier this month prompted a political row.
There was an outcry among MPs from all parties that the police action represented a fundamental breach of their right to hold the government to account.
Police had been asked by the Cabinet Office to investigate alleged leaks from the Home Office.