Boris Johnson has provided an "insufficient" response to an inquiry into his relationship with an American model turned technology entrepreneur, the London Assembly has said.
The prime minister is facing conflict of interest allegations following claims Jennifer Arcuri was given more than £100,000 in public money and privileged access to overseas trade missions led by Mr Johnson during his time as London mayor.
He has refused to deny outright that he had an affair with Ms Arcuri, 34, but previously told Sky News "everything was done with complete propriety" when quizzed on the allegations.
Mr Johnson submitted a response to the London Assembly, which is investigating the pair's links, on Tuesday night at what was said to be the end of a two-week deadline.
They had asked him for details and a timeline of all contact with Ms Arcuri, including social, personal and professional encounters during his period of office as London mayor.
The prime minister was also asked for an explanation of how their alleged personal relationship was disclosed and taken into account in any and all dealings with the Greater London Authority (GLA) and other parts of the GLA family.
The London Assembly, the capital's elected body, have now deemed Mr Johnson's responses to be "insufficient" and questioned his request for them to be kept secret.
Labour's Len Duvall, the chair of the London Assembly's oversight committee, said on Wednesday: "The role of the London Assembly is to ensure that City Hall is above question and we must abide by the ethos of complete openness and transparency.
"We did finally receive a response from Boris Johnson, through his solicitors, which they have indicated may not be published.
"At this stage we are respecting that, but we are seeking further clarification.
"Nothing in the response, in our opinion, reflects the need for confidentiality. In fact, the response is insufficient as far as our request for information is concerned.
"We are focused on our investigation and considering next steps.
"A number of options are open to us; they include speaking to various people and using our power of summons."
Mr Duvall added his committee was liaising with the Independent Office for Police Conduct, the police watchdog to which the allegations about Mr Johnson have been formally referred.
He added: "We're now formulating our response to the statements made in the letter and may make further statements once that response is finalised in the coming days."
A Tory source claimed the GLA have "given out false information to the media and are now leaking private correspondence".
"This is yet more evidence that this is a politically motivated attack, not a genuine investigation. The GLA hasn't followed due process," the source added.
Jon Trickett MP, Labour's shadow Cabinet Office minister, said: "With an issue as serious as potential abuse of public office, it is absolutely in the public interest that this letter be published.
"Boris Johnson might think he is above the law but he cannot hide from scrutiny. As a former prime minister said: sunlight is the best disinfectant.
"If he fails to answer these questions, he is showing contempt for the inquiry and the people of this country. This is about the integrity and honesty of the man who is the prime minister."
Mr Johnson has been referred to the IOPC because, as mayor, he was also the head of the mayor's office for policing and crime, a role equivalent to police and crime commissioner for the capital.
The Sunday Times first reported the allegations about Mr Johnson and Ms Arcuri.
The newspaper has since reported fresh claims that Mr Johnson wrote a letter recommending Ms Arcuri - then a 27-year-old student - for a £100,000 a year job as chief executive of Tech City, which was established to help technology start-ups in the capital.
A Number 10 spokesperson said: "We responded to the GLA well within the deadline. We hope they will follow proper process in this matter."