The BBC's Andrew Neil has issued a challenge to Boris Johnson to take part in a sit-down interview with him before next week's general election.
Mr Johnson is the only leader of a main party not to have faced a half-hour, prime-time BBC One grilling by Mr Neil.
The Conservative leader has denied claims he is avoiding scrutiny.
But Mr Neil addressed the PM directly at the end of his fourth leader interview at this election, with Brexit Party leader Nigel Farage.
"It is not too late. We have an interview prepared. Oven-ready, as Mr Johnson likes to say," he said, in a monologue.
"The theme running through our questions is trust - and why at so many times in his career, in politics and journalism, critics and sometimes even those close to him have deemed him to be untrustworthy.
"It is, of course, relevant to what he is promising us all now."
Mr Johnson has also declined an invitation to be grilled by ITV's Julie Etchingham, as part of her series of leader interviews.
'Hold to account'
Mr Neil said that no broadcaster "can compel a politician to be interviewed".
But he added: "Leaders' interviews have been a key part of the BBC's prime-time election coverage for decades.
"We do them, on your behalf, to scrutinise and hold to account those who would govern us. That is democracy.
"We have always proceeded in good faith that the leaders would participate. And in every election they have. All of them. Until this one."
Mr Neil then listed the questions he wanted the prime minister to answer.
These include whether he can be trusted to deliver on his promises for the NHS - and keeping the health service "off the table" in any post-Brexit trade talks with the US.
Mr Neil said he would also ask the PM about his claim that he has always been an opponent of austerity, another "question of trust".
He ended the monologue by saying: "The prime minister of our nation will, at times, have to stand up to President Trump, President Putin, President Xi of China.
"So it was surely not expecting too much that he spend half an hour standing up to me."
Labour leader Jeremy Corbyn, the SNP's Nicola Sturgeon, Lib Dem leader Jo Swinson and Brexit Party leader Nigel Farage have all faced a grilling by Mr Neil.
Jo Swinson apologised for supporting welfare cuts when she was part of the Lib Dem/Conservative coalition in her Neil interview.
Nicola Sturgeon was pressed about Scottish independence and the EU, and her party's record on the NHS in Scotland, while Nigel Farage was forced to defend his decision not to contest Tory seats.
Mr Johnson was quizzed by the BBC's Andrew Marr on Sunday, on why he had not yet agreed to be interviewed by Andrew Neil.
He denied avoiding prime-time scrutiny, saying he had done TV debates, interviews and a "two-hour phone-in".
Separately, on Thursday evening, The Labour Party complained about BBC bias, in a letter to Director General Tony Hall.
Labour's co-campaign coordinator Andrew Gwynne highlighted Mr Johnson's failure to be interviewed by Andrew Neil.
In his letter, Mr Gwynne claimed the Conservatives were being allowed to "play" the corporation, making the BBC effectively "complicit in giving the Conservative Party an unfair electoral advantage".
He said Labour had agreed Mr Corbyn's interview with Mr Neil based on the "clear understanding" that Mr Johnson had agreed the same terms.
"Instead, the BBC allowed the Conservative leader to pick and choose a platform through which he believed he could present himself more favourably and without the same degree of accountability."
The BBC is expected to respond in writing to the Labour complaint.
But a spokesperson said in a statement: "The BBC will continue to make its own independent editorial decisions, and is committed to reporting the election campaign fairly, impartially and without fear or favour."
In another development, the prime minister's team have confirmed that Mr Johnson will not find time for an interview with ITV before the general election.
He is the only leader of a major party to turn down the request from the channel's Tonight programme.
A spokesman for ITV said the programme had bid for Mr Johnson when the general election was called.
"They have contacted his press team on repeated occasions with times and dates offered to film an interview," the spokesman said.
"Boris Johnson's team have today confirmed he will not be taking part.
"The programme will instead feature a profile of the prime minister using fresh interviews with other contributors and archive footage."
ITV Tonight presenter Julie Etchingham has recorded an interview with Jeremy Corbyn, which was broadcast on Thursday evening.
Labour Party chairman Ian Lavery said: "Boris Johnson thinks he's born to rule and doesn't have to face scrutiny.
"He's running scared because every time he is confronted with the impact of nine years of austerity, the cost of living crisis and his plans to sell out our NHS, the more he is exposed."
Liberal Democrat Leader Jo Swinson said: "Boris Johnson must stop ducking scrutiny. His cowardly behaviour shows why he simply isn't fit to be prime minister."
She said it was "bad enough" that her party had been "excluded" from the BBC's head-to-head debate between Mr Johnson and Mr Corbyn, and "even worse that right now Boris Johnson won't be held properly to account for his lies and extreme Brexit plans".
Mr Johnson will face Mr Corbyn in a prime ministerial debate at 2030 GMT, on BBC One, on Friday.