Number 10 says Culture Secretary Tessa Jowell has the full support of Tony Blair, as questions continue over her husband's financial dealings.
Ms Jowell denies any wrongdoing
But Mr Blair's spokesman said Cabinet Secretary Sir Gus O'Donnell would want to "establish the facts" of the case.
Ms Jowell denies any conflict of interest over financial dealings involving her husband, David Mills.
But the Times says it has seen papers saying the Home Office hampered a probe intended to bring Mr Mills to trial.
Ms Jowell's husband, an international lawyer, denies taking a £344,000 bribe from Italy's Prime Minister Silvio Berlusconi.
The Sunday Times alleges it has identified a link between a loan secured on a house jointly-owned by the couple and the money which Italian prosecutors allege was a bribe.
Ms Jowell's involvement comes from co-signing a £408,000 mortgage on the North London home she jointly owns with Mr Mills.
It was reportedly paid off only weeks later - allegedly using money Mr Mills received from Italy, although Ms Jowell has categorically denied it was paid off with money from Mr Berlusconi.
"I agreed that we would take out a loan on our house. That is not unusual, it's not improper, and it's certainly not illegal," she told the BBC.
Mr Mills denies doing anything wrong and denies that the money came from anyone connected with Mr Berlusconi, saying that it came from another client.
A report into the payment by Italian prosecutors has been handed to a judge in Italy who will decide whether to prosecute.
Meanwhile, the BBC has obtained a copy of a letter written by Mr Mills to his accountant two years ago, in which he says: "I told no lies, but I turned some very tricky corners which kept Mr B out of a great deal of trouble."
He says that $600,000 was put into a hedge fund and refers to "the person connected to the B organisation".
Later he says: "I regarded the payment as a gift - what else could it be?"
The matter raises awkward questions for Ms Jowell.
Shadow Commons leader Theresa May has written to Sir Gus to ask if there had been a conflict of interest for the Cabinet minister under the ministerial code.
The code states that ministers should provide their permanent secretary "with a full list in writing of all interests which might be thought to give rise to a conflict.
The list should cover not only the minister's personal interests but those of a spouse or partner... of trusts of which the minister or a spouse... is a trustee or beneficiary".
The prime minister's spokesman said Sir Gus would reply to the Conservatives "when he's ready to" and that might "take a little bit longer".
Asked if Ms Jowell had Mr Blair's full support, the spokesman added: "I said, 'yes' yesterday and 'yes' today. Somehow my yes came across as no or maybe. I say 'yes' today."
However, the spokesman refused to say whether Ms Jowell had spoken to the prime minister about the affair or if Mr Blair had asked Sir Gus to investigate.
But Tony Wright, the Labour chairman of the influential Commons Public Administration Committee, said the matter was now "a great big mess" and repeated his calls for an independent person, away from government, to probe such issues.
BBC Political Editor Nick Robinson said the cabinet secretary's investigation was "intriguing" because "no specific allegations have actually been made suggesting Tessa Jowell has actually broken any rules at all".
"People will remember, of course, that it was his verdict on David Blunkett that really ended his career - not the prime minister's," he said.