Jeremy Hunt has said plans for a televised Conservative leadership debate three days after voting begins is making a “mockery” of the contest.
Mr Hunt said Boris Johnson had challenged him to a debate on ITV, scheduled to take place on 9 July.
He accepted, but then “realised” it would take place the day after party members received their postal ballots.
The pair will make their first leadership pitch directly to party members in Birmingham later.
Members of the Conservative party will receive their ballot papers between 6-8 July, with the new leader expected to be announced in the week beginning 22 July.
The foreign secretary said any debate should take place before voting starts.
Tory MPs whittled an initial list of 10 candidates down to two through several rounds of voting.
In the fifth and final round on Thursday, Boris Johnson came out on top with 160 out of the 313 votes cast. Mr Hunt received 77 votes and Michael Gove was knocked out with 75.
ITV’s programme will be the third televised debate of the campaign and the first in which the two finalists will go head-to-head.
Mr Hunt said: “It makes an absolute mockery of this leadership contest for the Conservative Party if people will actually have started voting before they have had a chance to see the two protagonists on TV.”
He said Mr Johnson had “challenged” him to an ITV debate, but then realised some members would have already cast their votes.
Mr Hunt did not make it clear whether he would be asking ITV to move its debate forward or seeking a broadcaster to stage one before 6 July.
But he added: “I think we should be doing debates early, we should be doing them often.”
Later on Saturday, the two contenders will attend the first of 16 leadership campaign events, known as hustings.
There they will face questions about Brexit and their wider policy plans from Conservative party members.
The newspaper said his partner, Carrie Symonds, was heard telling Mr Johnson to “get off me” and “get out of my flat”.
The Metropolitan Police said “there was no cause for police action”. A spokesman for Mr Johnson declined to comment.
Speaking on BBC Radio 4’s Today programme, former attorney general, Dominic Grieve, said “reliability and honesty” is important when it comes to the candidates’ character.
He said: “I think they matter in one’s private and personal life, and also they matter in one’s public life.
“People are going to have to weigh that up in respect of either of these two candidates.”
Mr Hunt endured a difficult day on the campaign trail on Friday when an inquiry was told he had failed to keep his promise to a man with terminal cancer during his time as health secretary.
The man’s widow said Mr Hunt had failed to deliver on a pledge to “sort out” a financial settlement for victims of the infected blood scandal.
The inquiry is looking at why 4,800 people with haemophilia were infected with hepatitis C or HIV in the 1970s and 1980s.
Mr Hunt’s spokesman said he had pushed for the inquiry.