However, he stated he is “aiming heart and soul” to get an agreement with Brussels, in the first hustings of the run-off to become Prime Minister.
Asked how he would go about Brexit negotiations, between now and October 31, Mr Hunt said: “A wise prime minister makes choices on the basis of the options that are actually available in front of them at the time.
“Now we don’t know what the situation will be on the 31st of October, but if there is no prospect of a better deal, if the European Union have been as inflexible as you say, and if no deal is on the table, then I will leave without a deal because we must keep our promise to the British people.
“But I would do so with a heavy heart, because of the risks to businesses up and down the country and the risks to the union.”
The foreign secretary said he has not met a single European leader who does not want to find a solution.
He said: “I think they would listen to a new British prime minister. And I think if we get this right we can get the deal we need.
“Send the right person and there’s a deal to be done. Send that right person and we can do what we all need to do, which is come back with something positive for our country.
“And that’s what I want to do.”
Mr Hunt added: “If we got to the 31st of October and the EU have not shown any willingness to negotiate a better deal that can get through the House of Commons, that’s not going to trap us in the Customs Union, then my judgment is that weighing those difficult options up, the political risk of no Brexit is far worse than the economic risk of no deal.”
Mr Hunt said he would take the UK out of the European Union in that situation “100 per cent”, but said it would not be his choice.
His comments came as he and his rival Boris Johnson addressed a hustings on Saturday.
At the hustings, Mr Johnson promised to “get Brexit done”, telling the audience he was the man to “unleash on the project.”
Mr Johnson told Tory members: “The hour is darkest before dawn.
“And I am here to tell you that in all confidence we can turn this thing around.”