The prime minister was accused in a newspaper investigation over the allocation of public money to a model turned technology entrepreneur.
He refused six times to comment directly on the allegations to journalists flying with him to the United Nations General Assembly in New York.
But, as the claims threatened to overshadow his talks, the PM briefly expanded on his position.
“Everything was done with complete propriety. Completely in the normal way,” he said in an interview on Tuesday.
He said he was “very proud” of his time as mayor, citing his work “banging the drum” for the capital and the nation.
On the RAF Voyager, the PM declined to deny the allegations centring on his association with Jennifer Arcuri.
The Sunday Times reported that Arcuri, an American who moved to London seven years ago, was given £126,000 in public money and was treated to privileged access to three foreign trade missions led by Johnson.
The PM declined to clarify the nature of his relationship with her and declined the opportunity to deny any allegations in the report.
He did not directly respond to six questions, including whether the allegations could be solved with a public inquiry.
When asked to clarify the nature of their relationship, he replied: “If you will forgive me, we are going to talk exclusively about what we are doing here in the UN.”
Labour has called for Johnson to fully explain the matter.
“Boris Johnson must now give a full account of his actions in response to these grave and most serious allegations of the misuse of public money in his former role as mayor of London,” shadow Cabinet Office minister Jon Trickett said.
“The public has a right to know how and why these funds were used for the benefit of a close personal friend without, on the face of it, legitimate reason.”
Arcuri, 34, did not comment to the Sunday Times about the nature of her relationship with Johnson.
“Any grants received by my companies and any trade mission I joined were purely in respect of my role as a legitimate businesswoman,” she said in a statement to the paper.
The newspaper investigation reported that Arcuri’s business received £10,000 in sponsorship from an organisation overseen by Mr Johnson as mayor in 2013.
A further £15,000 was said to have come in 2014 and a £100,000 grant from the Department for Digital, Culture, Media and Sport earlier this year.
Downing Street has declined to comment.