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.
The foreign secretary accepted his invitation but now says a TV debate should be held before voting starts.
The pair will make their first leadership pitch directly to party members in Birmingham later.
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Tory MPs whittled an initial list of 10 candidates down to those 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 and Michael Gove was knocked out with 75.
Conservative party members will now decide who will become party leader – and prime minister – via postal voting during July.
The new leader is likely to be announced on the week beginning 22 July.
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.”
“Boris challenged me to the ITV debate until I realised that that debate is so far ahead that people will already have started voting before it happens.”
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” and a spokesman for Mr Johnson said: “No comment”.
Mr Hunt endured a difficult day on the campaign trail on Friday when an inquiry heard he had failed to keep his promise to a man with terminal cancer during his time as health secretary.
The inquiry is looking at why 4,800 people with haemophilia were infected with hepatitis C or HIV in the 1970s and 1980s.
A spokesman for Mr Hunt said he had “pushed for this landmark inquiry”.
Tory leadership: Hunt seeks change to TV debate schedule}