Jeremy Hunt says Boris Johnson should have a “very big role” in his future cabinet if he wins the Tory leadership contest – despite his competitor refusing to make the same offer.
The foreign secretary told a hustings in Exeter he would love Mr Johnson on board as he was an “enormous talent”.
But his rival told the event he was “not making commitments to anybody”.
Mr Johnson also denied reports that he had offered a job to Home Secretary Sajid Javid.
He told the hustings that, if he made any comments on his prospective cabinet, he would be seen as “measuring the curtains” for 10 Downing Street and there was “still a long way to go” in the contest.
The two contenders are taking part in 15 hustings across the country as Conservative Party members decide on their party’s next leader – and the next UK prime minister.
The 160,000 members will begin voting next week and the winner is expected to be announced on 23 July.
The pair were quizzed by the audience on a number of issues, from Brexit and Russia, through to animal welfare and the sugar tax.
Asked by an audience member whether he would give Mr Johnson a role in his government, Mr Hunt made a joke that he could be his “secretary of state for collective responsibility”.
But after his “light-hearted dig”, he added: “Of course I would love to have Boris in my cabinet.
“Boris is someone of enormous talent. He has changed the course of our history through his leadership of the Leave campaign and he should always have a very big role in taking things forward.”
Mr Hunt also said he would be happy to serve under Mr Johnson, adding: “We are in an incredibly difficult situation and I think whoever doesn’t win in this contest needs to put their shoulder to the wheel and serve loyally the winner, so that we can get through this, get to the other side and give the country all the exciting things we want to do.”
But asked the same question, Mr Johnson said there was “a wealth of talent on the Conservative benches”.
Pushed by the hustings’ host, LBC radio presenter Iain Dale, on the convention of giving a losing leadership opponent a cabinet position, Mr Johnson added: “I have a very, very high regard for Jeremy.
“It sounds to me eminently fair and logical, but I am not making commitments to anybody because you would not expect that.”
The pair also discussed a story in the Sun that claimed the government was looking to extend its “sugar tax” on soft drinks to milkshakes.
Mr Hunt said the the country needed to “tackle the obesity crisis”, but the “quickest way” was to target manufacturers of unhealthy food to reduce the level of sugar.
“You threaten them,” he said. “You say, we would be prepared to legislate if you don’t play ball.
“But my experience is, if you make that threat, you don’t actually need to follow through with the dreaded milkshake tax.”
Mr Johnson mocked his own weight while answering the question, but said he was “very, very reluctant to imposes taxes… that clobber those who can least afford it”.
He added: “What we should be doing, if you want kids to lose weight, is make the streets safe… encourage kids to walk and cycle to school, which will help them to lose weight as well, and generally take more exercise and be more active”.
And Mr Johnson was also asked about accusations in the Daily Mail that he called the French “turds” during the filming of a BBC One documentary about the Foreign Office.
The newspaper accused the BBC of cutting the clip from the programme – which aired last November – at the request of the Foreign Office, who worried the comment would make Anglo-French relations “awkward”.
Mr Johnson said he had “no recollection of this comment”, adding: “Perhaps what everyone will want to know is, can I get a fantastic deal for our country from our French friends, can we go forwards in a friendly, collegiate way, and yes, of course we can.”
A spokeswoman for the BBC said: “The programme set out to reflect the realities of life inside the Foreign Office. The production team made judgments about what was in the programme and they are satisfied that the programme achieves its ambitions and has the content they wanted.”
The Foreign Office declined to comment.