Mr Hunt said he believed the issue of the border could be resolved through the use of technology to avoid the need for physical checks.
He dismissed arguments by the EU that the technology which would be required did not yet exist.
"I think one of the reasons they tell us that is because frankly it would be easier for them and better for them if we stayed inside the customs union," he said.
Both candidates insisted they would work to restore the powersharing government - which has been suspended for more than two years - to Northern Ireland as soon as possible.
Mr Johnson said he would "energise" the talks between the parties while Mr Hunt said the lesson of the Good Friday Agreement was that any progress required the personal involvement of the prime minister.
"Theresa May has been very committed to Northern Ireland and to the union but I give you this commitment that I too as prime minister will put in the time personally to get that assembly back up and running," he said.
Mr Johnson and Mr Hunt also both insisted the issue of legislation to allow abortion and same-sex marriage in Northern Ireland - both opposed by the Tories' allies in the DUP - had to be a matter for a restored Stormont assembly.
Mr Hunt said that while he personally supported legal change on both matters, there had to be an element of "social consent" if it was to go forward.
"This is a devolved matter and I think the best way to resolve this is to get the Assembly back up and running and to establish a consensus in the province so that we can go forward on these very difficult issues," he said.
Mr Johnson said both issues were "pre-eminently a matter for the people of Northern Ireland".
"That is why, to risk sounding like a cracked record, I hope the government of Northern Ireland can be resumed as soon as possible so this issue can be decided in the forum where it properly belongs," he said.
25 July, 2021 Need to say something? The lingering Mercury/Pluto link can give you the determination to strike up a conversation. A matter may shift as a result, and things might never be quite the same again, whether this relates to a big or small issue. But it could clear the air and pave the way for bigger and better things. And you'll have the time and space for new plans and projects, Aries.
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