Grant Shapps said that he will not “seek to defend” the reports and acknowledged his own upset over the revelations.
It is the latest in a long line of allegations of rule-breaching gatherings held in Downing Street during the strict coronavirus measures.
Speaking to Sky News this morning, the Transport Secretary said: “It was his (Boris Johnson’s) birthday and these are people that he worked with all the time.
“As I said, I don’t seek to defend it. This is for Sue Gray to decide on whether this was appropriate, she’ll make the recommendations.
“I think we can be pretty clear that the Prime Minister didn’t present the cake to himself. This is somebody coming in with that cake and I’ve explained to you that I’m furious with everybody who broke the rules.”
Speaking later to BBC Radio 4, Mr Shapps said that birthday events should have been postponed “in all cases.”
He was pointed to a letter sent to Boris Johnson by then seven-year-old Josephine Booth in March 2020 who told the Prime Minister she had cancelled her own party due to coronavirus.
“I think that she did exactly the right thing.” Mr Shapps said.
“I think that should have been done in all cases, and I don’t seek to say otherwise.”
On Monday evening, Downing Street conceded staff “gathered briefly” in the Cabinet Room following a meeting after it was alleged 30 people attended and shared cake despite social mixing indoors being banned.
ITV News reported the Prime Minister’s wife, Carrie Johnson, had organised the surprise get-together complete with a chorus of “Happy Birthday” on the afternoon of June 19 2020.
Interior designer Lulu Lytle admitted attending but insisted she was only present “briefly” while waiting to talk to Mr Johnson about the lavish refurbishments she was carrying out to the couple’s flat above No 11.
A Downing Street spokeswoman said: “A group of staff working in No 10 that day gathered briefly in the Cabinet Room after a meeting to wish the Prime Minister a happy birthday. He was there for less than 10 minutes.”
ITV News also reported later that evening family friends were hosted upstairs to further celebrate the Prime Minister’s 56th birthday in his official residence.
No 10 said: “This is totally untrue. In line with the rules at the time the Prime Minister hosted a small number of family members outside that evening.”
However, Mr Shapps suggested that the public may not think that the events were a party, having told BBC Breakfast: “I think most people would think of a party as being an arranged event rather than something where on somebody’s birthday in the office that they work in with the people that they always work with, someone says ‘it’s your birthday here’s a cake’.
“But that is for Sue Gray to get to the bottom of, I do agree and understand why – not least from my own personal experience – this would cause upset.”