Sonia Khan, an adviser to Mr Javid, was escorted from Downing Street by police on Thursday after her security clearance was withdrawn following a showdown with the Prime Minister’s chief aide Dominic Cummings.
Mr Javid was reportedly “absolutely furious” and confronted the Prime Minister over the issue on Friday.
He told him that Mr Cummings had undermined his authority, and demanded the return of Ms Khan, according to The Times.
But he told BBC Radio 4’s Today show this morning that he had a “fantastic relationship” with Mr Johnson, as he sought to play down the row.
Asked about the abrupt firing, Mr Javid said: “I am not going to discuss any personnel issues, it would be inappropriate.
“I think my views are well understood.
“The relationship is fantastic with the Prime Minister.”
Asked about Mr Cummings, the Chancellor said: “The Prime Minister is my boss and we work together, along with other Cabinet colleagues, to deliver, so I am not here to talk about particular individuals that are advisers in Downing Street.”
Ms Khan was questioned about her “contact with individuals” seen as actively working against the Government that had resulted in a “loss of confidence”, a Whitehall source told the Evening Standard.
According to witnesses, Mr Cummings demanded to see Ms Khan’s phone before reportedly calling police.
One witness said they “marched her out of No 10 as she protested her innocence”.
The incident comes just days before Mr Javid delivers his first major announcement as Chancellor when he unveils the details of the autumn spending review to MPs next week.
Pressed on claims by Labour that Mr Cummings is in charge of the Treasury, Mr Javid said: “The Labour Party, they are our opponents and they will say all sorts of nonsense all the time, and I am used to it.”
A Metropolitan Police spokesman said: “On Thursday, 29 August, a police officer stationed at the door of No 10 Downing Street escorted a woman from the front door to exit gates as she did not have a security pass at the time.
“This is standard practice if a visitor does not have a pass.
“The woman was not arrested.”
Downing Street declined to comment on the matter.