Rachel Reeves is facing calls to be sacked after she admitted breaking a London borough's housing rules when renting out her family home.
The Chancellor told Prime Minister Sir Keir Starmer she did not obtain the required "selective" rental licence for her East Dulwich home when she moved into No 11 Downing Street after Labour won the election.
Sir Keir has given his backing to Ms Reeves after consulting his independent ethics adviser, Sir Laurie Magnus.
In a letter to the Prime Minister, Ms Reeves "sincerely" apologised for her "inadvertent error" of not obtaining the licence, which was revealed by the Daily Mail.
An exchange of letters between the PM and Ms Reeves revealed they had met to discuss the matter on Wednesday evening, after it came to light.
Ms Reeves told the Prime Minister that "regrettably" she and her family were not aware a licence was needed in their area of the Southwark borough.
Southwark Council requires people renting out their properties in certain areas to get one of the licences in advance.
The council's website states: "You can be prosecuted or fined if you're a landlord or managing agent for a property that needs a licence and do not get one."
Reeves' family home in London was put up for rent after Labour won the election in July 2024 for £3,200 a month.
The Chancellor is understood to have relied upon the advice of a letting agent, which said it would advise if a licence was needed.
Ms Reeves told Sir Keir: "This was an inadvertent mistake. As soon as it was brought to my attention, we took immediate action and have applied for the licence."
She added: "I sincerely apologise for this error and I would be happy to answer any questions you may have."
In his reply, the Prime Minister said he had consulted his independent adviser Sir Laurie, adding: "He has advised me that in relation to your inadvertent failure to secure the appropriate licence for your rental property - and in light of your prompt action to rectify the position, including your apology - further investigation is not necessary.
"The Ministerial Code makes clear that in certain circumstances, an apology is a sufficient resolution. It is important that all ministers are able to acknowledge where they consider themselves to have fallen below the standards expected of them.
"I am satisfied that this matter can be drawn to a close following your apology."
The Prime Minister said it was "regrettable that the appropriate licence was not sought sooner" but said he believed the Chancellor was "treating this matter with the urgency and seriousness it deserves".
Sir Keir's decision to back Ms Reeves comes less than a month until the Budget, in which she is expected to have to make difficult fiscal decisions.
It also follows on the heels of several high-profile exits from Government as a result of scandals.
Among these was Angela Rayner, the former deputy prime minister and housing secretary, who resigned following a row about her tax affairs.
Lord Mandelson was also sacked as ambassador to Washington after details of his relationship with the dead paedophile financier Jeffrey Epstein came to light.
Conservative leader Kemi Badenoch had earlier called on the Prime Minister to "launch a full investigation" into Ms Reeves' error.
She added: "He once said 'lawmakers can't be lawbreakers'.
"If, as it appears, the Chancellor has broken the law, then he will have to show he has the backbone to act."
A Conservative spokesperson added: "Rachel Reeves has broken the law and broken the ministerial code, but Keir Starmer is too weak to sack her.
"Keir Starmer pledged to restore integrity to politics, but now he's laughing in the face of the British public. He should grow a backbone and sack the chancellor now."
Daisy Cooper, Lib Dem deputy leader, said: "The Chancellor is meant to be delivering growth but the only thing she appears to be growing is the Government's list of scandals.
"Just weeks before the Budget, this risks seriously undermining confidence in this Government and its ability to focus on the urgent tasks at hand."