Rishi Sunak declined to publicly back Home Secretary Suella Braverman after allegations she asked civil servants to help her avoid incurring points on her licence for speeding.
The Prime Minister was facing renewed calls on Sunday to launch an investigation into the Cabinet minister after he declined to set out whether he will order a probe.
Mr Sunak did not express support for Mrs Braverman when asked three times at a press conference in Hiroshima, where he attended talks with G7 leaders and Ukraine’s Volodymyr Zelensky.
“I think you can see first hand what I have been doing over the last day or so but I understand that she’s expressed regret for speeding, accepted the penalty and paid the fine.”
However, a No 10 spokeswoman later insisted he does “of course” have full confidence in his Home Secretary, responding to a message: “Yes, he does.”
Mr Sunak, who left the press conference to fly back to London as planned, is expected to speak to Mrs Braverman as well as Cabinet Secretary Simon Case after his return.
He expressed his frustration at being asked whether he would ask his ethics adviser Sir Laurie Magnus to investigate the claims.
“Did you have any questions about the summit?” he asked.
The Sunday Times reported that Mrs Braverman asked Home Office aides to help organise a one-to-one driving awareness course.
Officials refused the request so Mrs Braverman allegedly turned to a political aide to assist her in attempting to arrange an alternative to having to attend a course with other motorists.
She was caught speeding outside London while she was Attorney General last summer.
The newspaper reported that a number of requests were made to a speeding awareness course provider by an aide, including asking if the senior Conservative minister could do an online course, but use an alias or have her camera switched off.
Mrs Braverman ultimately chose instead to accept three points on her driving licence.
He told the BBC’s Sunday with Laura Kuenssberg programme: “You shouldn’t do it in the first place but if you do get caught, you just take the medicine.”
Shadow home secretary Yvette Cooper demanded an “urgent investigation” by Sir Laurie to see whether Mrs Braverman breached the ministerial code.
After Mr Sunak’s press conference, the Labour MP said: “Not good enough Prime Minister.
“The Home Secretary is alleged to have tried to abuse her position to avoid a legal penalty.
“Are you really too weak to even set up an investigation?”
Liberal Democrat home affairs Spokesperson Alistair Carmichael said every second Mrs Braverman is not under investigation is “another blow to the integrity of this already sleaze-ridden Prime Minister”.
Sir Laurie cannot launch an investigation without Mr Sunak’s approval but a breach of the ministerial code is often a resigning matter.
A source close to Mrs Braverman told the PA news agency the speeding ticket and subsequent arrangements for dealing with it were reported to the Cabinet Office at the time.
They said she was keen to arrange a course because of concerns her insurance premium potentially could increase.
Mrs Braverman resigned in October after sharing a sensitive document with a Tory backbencher from a personal email without permission.
But Mr Sunak reappointed her just six days later when he entered No 10.
A spokesman for the Home Secretary said: “Mrs Braverman accepts that she was speeding last summer and regrets doing so.
“She took the three points and paid the fine last year.”
A motorist can be banned from driving if they have 12 or more penalty points on their licence.