The UK's top civil servant has admitted having an "informal conversation" about potential roles for the PM's wife with a royal charity, after being prompted by a former Downing Street colleague.
But Simon Case said he had not recommended that the Duke and Duchess of Cambridge's Royal Foundation give Carrie Johnson a position.
There had been "no improper conduct" on his part, he added.
However, Labour said the PM had "serious questions" to answer.
In her letter asking Mr Case what had happened, the party's deputy leader, Angela Rayner, said Boris Johnson had to address claims of "impropriety and conflict of interest".
On Wednesday, during Prime Minister's Questions, Mr Johnson did not deny reports he had spoken to aides about a government post.
It has been reported that, while foreign secretary in 2018, Mr Johnson tried to hire his future wife, with whom he was already in a relationship, as his £100,000-a-year chief of staff.
In her letter to Mr Case, the cabinet secretary, Ms Rayner wrote: "There are now serious questions for the prime minister to answer about potentially impropriety and conflict of interest in his lobbying for a high-paying tax-funded job for his partner in 2018, Carrie Johnson."
This and the other reports raised "serious questions about sleaze and corruption" in Downing Street, she added.
"It is clearly inappropriate that the prime minister should be the judge and jury in his own case, so I ask you to confirm that this matter will be subject to an independent probe and fully investigated," Ms Rayner also wrote.
In response, Mr Case wrote: "I did not recommend Mrs Johnson for any role.
"In autumn 2020 a former member of the No 10 team asked about opportunities for Mrs Johnson with environmental charities.
"I was happy to have an informal conversation with someone involved with the [Royal Foundation's] Earthshot Prize about what roles were available, as I would have done for anyone with relevant experience who was keen to get involved with charity work."
Mrs Johnson, a former head of communications for the Conservative Party, married Mr Johnson in May last year and they have two children together.
She has also worked for the Oceana marine conservation group and the Aspinall Foundation animal rights charity.