Jeremy Hunt has accused the BBC of “caving” to Boris Johnson by planning a Tory leadership debate after most party members will have already voted.
The foreign secretary said on Tuesday he had been invited to take part in a head-to-head on 16 July.
But postal ballots will be delivered to members this week and it is expected that they will be quick to vote.
Lynton Crosby is the political strategist behind many of Johnson’s campaigns, including his two successful bids for London mayor.
A BBC spokesperson said: “The BBC is keen to host a Question Time Special debate with both remaining candidates and has been trying to agree a date which works.
“Both candidates have already taken part in the first BBC debate, both have been interviewed by our political editor, and both have agreed in principle to participate in a Question Time special. We don’t think it’s reasonable to empty chair people who have already participated in interviews and debates and have agreed to take part again.
“Clearly any date needs to fit in with the candidates’ existing commitments such as hustings and other TV appearances.
“July 16 is before the last Conservative hustings and the voting will still be open. But, crucially, our debate is about the next Prime Minister and we think it’s important both candidates speak to the whole of the UK, as well as the members of the Conservative Party.
“We have also invited both candidates to be interviewed consecutively by Andrew Neil for a BBC One special.”
Hunt is seen to be facing an uphill battle to beat Johnson in the contest and has subjected himself to media scrutiny in an attempt to ram home the message that Johnson is in hiding.
Johnson refused to take part in a debate hosted by Sky News last night and the broadcaster devoted the entire hour to interviewing Hunt.
Johnson instead took party in a conference call with party members in which he told them he was the “right guy now to deliver for our party”.
Both men will face questions about their Brexit plans at a hustings in Northern Ireland later this morning.
Hunt received a boost to his campaign this morning when former Tory leader William Hague said he was “logically and inescapably drawn to vote” for the foreign secretary.