Hunt is among 10 candidates hoping to become the new leader of the Conservative party after Prime Minister Theresa May last week confirmed she will stand down on 7 June.
A leadership contest is expected to follow immediately.
Hunt, who voted to remain in the EU in 2016’s Brexit referendum, was pitching himself as a moderate candidate against favourite Boris Johnson’s repeated support for a no-deal Brexit.
Housing minister Kit Malthouse, who announced his candidacy over the bank holiday weekend, said today the UK must prepare for a no-deal scenario.
“We don’t want no deal, we want a deal, but we will be ready for it,” he told BBC Radio 4’s Today programme. “An extension [beyond 31 October] would be extremely difficult.”
London’s former deputy mayor, whose Malthouse compromise won hard Brexiters’ backing with a pledge to avoid a hard border on the island of Ireland, warned the EU may force Britain into leaving without a deal.
“We have to prepare for no-deal on the basis that the EU may well choose it on their and our behalf,” he said. “We need to get to 31 October ready and able to take no deal if we want to, we need to have some honest conversations about the industries that are going to be affected.”
Meanwhile, health secretary Matt Hancock has claimed it is “mission critical” to deliver Brexit before a general election after the Tories’ weak performance in last week’s European elections.
The party came fifth in the UK, behind the Green party, to return just four MEPs to the European parliament.
Writing in the Daily Mail, Hancock said: “It’s not that most people want a no-deal Brexit, but because so many rightly think we should have left by now and want us to get on with it. So it is mission critical we deliver Brexit before any general election.”