The foreign secretary also made the claim he could negotiate a new deal with the bloc that would do away with the need for the Irish backstop - despite such a route already being repeatedly dismissed by the EU.
Mr Hunt came second in the first round of voting among Tory MPs in the party's leadership contest, achieving 43 backers, but still considerably behind Boris Johnson, who received 114 votes.
In an attempt to pitch himself as the alternative to the his predecessor at the Foreign Office, Mr Hunt said he was not willing to pledge a "hard stop, any cost" exit from the EU on 31 October - the current deadline for Brexit.
He told the BBC's Andrew Marr programme this would effectively mean committing the country to a no-deal scenario, "or an election if parliament chooses to stop that".
Asked directly what the "final date" would be of Britain leaving the EU, Mr Hunt replied: "I'm not committed to a 31 October, hard stop at any cost because I don't think we can make that guarantee.
"If we do make that guarantee, if we go with the wrong approach then you are committing us to nothing other than a no deal Brexit.
Pressed on whether the UK would "definitely" be out of the bloc by the end of the year, he replied: "A wise prime minister makes choices on the basis of the choices that are actually in front of them.
"By the time you get to the 31 October we may have parliament having changed the law in particular ways, we may have a new European Commission, we may have made very good progress in the negotiations.
"I've been very clear, if there is no prospect of getting a deal that can get through parliament on 31 October, then I will be prepared to leave without a deal."
He added: "If there's no prospect of a deal, then I'm out. If there is a prospect of a deal – what I'm saying is the difference between me and Boris is that I'm saying I would try for a deal.
"I'm not going to create a set of circumstances that makes it all but impossible to get a deal because I think we should be offering the country some better choices."
His comments will likely infuriate the most hardline Brexiteers in the Conservative Party - just moments before Dominic Raab, who is also running for the leadership, warned the party would be "toast" if it fails to exit the EU by 31 October.