Ahead of a hustings event in Perth that will see both Tory leadership candidates take questions from Scottish members, Mr Hunt launched an attack on his rival Boris Johnson’s plan to protect the Union.
Mr Johnson says he will personally ensure that policies are “sense and stress tested” for the whole UK.
The Foreign Secretary said: “My commitment to the Union is second to none, but I don’t want to be a Prime Minister who declares myself “minister of the Union” and thinks that’s enough.”
Mr Hunt added: “Scotland has excelled at promoting ideas and inventions globally. Where there is an existing market advantage – in Fintech, BioTech, or the food and drink industry – I will seek to drive that home.
“That means a review of spirit duty to establish the best path to economic growth and the most tax revenue. Scottish whisky has an in-built, natural and nostalgic advantage over its competitors. But we cannot get complacent, there are markets that must be seized in South America and Asia.
“If we deliver a good Brexit deal and follow it with the right trade deals, we can continue the Scottish whisky boom.”
Ahead of the Scottish hustings, Theresa May’s deputy warned a no-deal Brexit would put “much greater strain” on the UK’s ability to stay together.
Cabinet Office Minister David Lidington, who backs Mr Hunt for the leadership, said: “The Union is under greater strain than I have ever seen in my lifetime.
“The threat to the Union, in my view, comes not just from Scottish nationalism, or pressure for Irish unification, it comes from indifference amongst English opinion... I think there is a sense in which we take the Union for granted.
“There are too many people in England, including in my party, who assume that you can be dismissive of the contribution that Scotland or Northern Ireland makes.”
Meanwhile, Brexit Party MEP Ann Widdecombe was criticised after comparing Brexit to slaves rising up “against their owners” in a speech to the European Parliament.