Mr Grieve refused to say whether or not he thought Mr Quick should continue in charge of the leaks inquiry, telling the BBC Mr Quick should make the "professional judgement" himself about whether he still had the "necessary objectivity" to continue.
And asked what he thought had prompted Mr Quick's comments, Mr Grieve said: "I can only assume that he was both angry and stressed because of the possible compromising of his security, and that as a result he came out with these intemperate and in truth completely deluded comments about the Conservative Party."
Mr Quick, who is heading the leaks investigation which saw senior Tory MP Damian Green arrested last month, said on Sunday he had been forced to move his family after a published newspaper article 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."
He later withdrew claims that the Conservatives had acted in a "corrupt" way, and issued the full apology on Monday in a statement.
"I have now reflected on the comments I made yesterday at a difficult time for me and my family. I wish to make clear that it was not my intention to make any allegations, and retract my comments," he said.
Conservative leader David Cameron had earlier called during an interview on London's LBC radio for Mr Quick had "to withdraw what is a completely baseless allegation... 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".
He added that 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".
Home Secretary Jacqui Smith, asked about the row during a visit on Monday, said: "I know Bob has now retracted some of the things that he said over the weekend and I think the most important thing is that he is able to get on with the job of keeping this country safe, which is what he does day in, day out as our most senior counter-terror police officer."
The acting commissioner of the Met, Paul Stephenson, said he was pleased that "a line has now been drawn under this matter".
But Liberal Democrat home affairs spokesman Chris Huhne said Mr Quick should step back from his role leading the leak inquiry.
"For the sake of the Met it would make sense for someone else to be overseeing the remainder of this inquiry," he said.
The arrest of Mr Green and the search of his home and offices 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.
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