Speaking at a leadership hustings in Colchester on Saturday, he said: “Maybe I will pay a political price for being honest with people.
“But the reality is that we face a hung parliament with people – not just in the Labour Party but in our own party – absolutely determined to stop us leaving without a deal.”
His comments come after he told the BBC’s Andrew Neil that he was not prepared to make a commitment when it was clear parliament could block it.
He said prime ministers should “only make promises they know they can deliver”.
His leadership rival, Boris Johnson, seized the opportunity to say another delay would be “insane”, leading Mr Hunt to confess such honesty might have cost him the race.
In the interview, Mr Hunt said he would not give a commitment when pressed on whether the UK would be out of the EU by Christmas but Mr Johnson repeated his pledge to stick to the new Brexit deadline of 31 October.
The two men faced two sets of hustings on Saturday, one in Wyboston in Bedfordshire in the morning and an afternoon quizzing from their party members in Colchester, Essex.
While some may feel the hustings, which are in their final stretch, are like groundhog day, campaigners say it can be important to have the same things repeated.
Ruth Betson, a supporter of Mr Johnson, told Sky News: “I think people need to know the candidates have the same answers over and over again, so that they are giving their pledge and their promise.”
Scott Pepe, who backs Mr Hunt, said people were turning up across the UK “quite undecided”.
He said: “I think when you hear the answers to the questions it’s clear that Jeremy has a greater grasp of the detail and an actual plan to deliver.”
In Wyboston, Mr Johnson promised party members he would “toughen up” measures with “current illegals” while showing compassion to new applicants seeking refuge in the UK.
Mr Hunt talked about cutting corporation tax to 12.5%, the same level as in Ireland, and said it would be part of a good strategy for no-deal Brexit planning.
During the course of the day, both leadership candidates gave their backing for press freedom, following remarks from Metropolitan Police Assistant Commissioner Neil Basu that news outlets should avoid publishing any more leaked documents.
Mr Johnson told Sky News it was wrong for police to have a say on the issue, adding: “Media organisations should feel free to bring important facts into the public domain.”
Mr Hunt tweeted that he would “defend to the hilt the right of the press to publish those leaks if they receive them and judge them to be in the public interest: that is their job”.
At the Colchester hustings, party members suggested Mr Johnson was the candidate to cheer people up, but that Mr Hunt was a details man.
Anne Allan, 76, from Colchester, said: “We’ve had three years of being sneered at and basically treated in a very sort of defeatist way.
“I think we’ve reached the stage where we need someone just to cheer us up.”
While some attended the hustings having already voted, others seemed to have gone along in order to help make up their minds.
Mark Armitage, who lives near Sudbury in Suffolk, said: “In the Tory party, you’ve got a choice of two different types of leaderships and it will be interesting to see who comes out of this [on top].
“It sounds like Boris is going to win anyway, who knows.”