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 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.
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 entered 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."Compare the candidates' policies and careers Select a topic and a candidate to find out more BREXIT TAX AND SPENDING HEALTH AND EDUCATION CAREER BREXIT Jeremy Hunt Foreign Secretary - Would leave the EU with no deal, but it's not his preferred option. - Wants changes to the Irish backstop and proposes sending a new negotiating team to Brussels. - Wants to make changes to the Withdrawal Agreement and thinks it's possible to get them done by 31 October, but has not ruled out an extension. Boris Johnson Backbencher - Wants to leave on 31 October, the deadline for Brexit set by the EU, with or without a deal. He admits a no-deal exit will cause "some disruption" but says the "way to get a good deal is to prepare for no deal". - Wants to remove the backstop from any deal and replace it with "alternative arrangements". - Says he would withhold the £39bn "divorce" payment the UK is due to give the EU as part of the negotiated deal. He says the money will be retained until there is "greater clarity about the way forward". TAX AND SPENDING Jeremy Hunt Foreign Secretary - As an entrepreneur, he wants to turn Britain into the next Silicon Valley, a "hub of innovation". - Pledged to slash business taxes to the lowest in Europe to attract firms to Britain after Brexit and reduce corporation tax. Boris Johnson Backbencher - Pledges to cut income tax for people earning more than £50,000 by raising the 40% tax threshold to £80,000. - Says it will benefit three million people and would cost £9.6bn a year. - Plans to pay for the cut partly from a pot set aside by the Treasury for a possible no-deal Brexit, and partly by increasing employee National Insurance payments. HEALTH AND EDUCATION Jeremy Hunt Foreign Secretary - Mental health support in every school and a crackdown on social media companies that fail to regulate their content. - A cut in interest rate paid on tuition fees. - Long term plan to provide more funding for the teaching profession in return for a guarantee that no one leaves the education system without a "rigorous qualification" sufficient to work up to at least the average salary. Boris Johnson Backbencher - Promises to raise spending on secondary school pupils to £5,000 each. - Called the funding gap between some schools in cities compared to those in rural areas a “disturbing reality”. - Has previously said money spent on the EU could be put into the NHS. CAREER Jeremy Hunt Foreign Secretary - The foreign secretary campaigned to remain in the EU during the 2016 referendum, but has since been reborn as a Brexiteer. - He even suggested, to widespread criticism, that the EU was like the Soviet Union. However, he has said his party would be committing “political suicide” if it tried to push through a no-deal Brexit. - An MP for South West Surrey since 2005, Mr Hunt was made culture secretary under the coalition government in 2010 and oversaw the 2012 London Olympics before becoming health secretary. - In 2018, he became the longest-serving health minister, and arguably one of the most controversial, since the NHS was created, completing six years in the role. During his tenure, he clashed with unions over contracts for junior doctors, who took part in a series of walkouts in 2015. Boris Johnson Backbencher - The 55-year Eton and Oxford-educated former political journalist has coveted the top job for many years, but was beaten to No 10 by his contemporary David Cameron. - After eight years as mayor of London, he returned to Parliament as MP for Uxbridge and South Ruislip in 2016. - A leading Brexiteer, Mr Johnson had been at odds with Theresa May’s Brexit vision for some time before he eventually quit as foreign secretary in protest last year. - Polls suggest he is a popular figure with members of the wider Conservative party.
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.
Mr Johnson featured on most of following reports by the Guardian that after neighbours reported "slamming and banging".
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 he had failed to keep his promise to a man with terminal cancer during his time as health secretary.
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".