Tory leadership hopefuls have come under fire over hard-line promises scrap the Irish backstop, which sent the pound plummeting amid growing concern about a no-deal Brexit.
In the wake of the remarks, sterling plunged to a six-month low against the euro and approached two-year lows against the dollar on Tuesday.
The pound weakened by 0.5 per cent on Tuesday to $1.2455, a six-day low. If it falls below $1.2439 it would sink to its lowest in more than two years, excluding a flash crash earlier this year.
As thousands prepare for their summer holidays, the pound fell 0.3 per cent to 90.25p against the euro, the lowest since January 11.
Both candidates have already refused to rule out a no-deal Brexit, with Mr Johnson pledging to take the UK out of the bloc on 31 October, with or without a deal.
Brussels insists that the backstop - which prevents a hard border on the island of Ireland - must be a part of any Brexit deal.
But Mr Johnson told The Sun's leadership debate: "No to time limits or unilateral escape hatches or all these elaborate devices, glosses, codicils and so on that you could apply to the backstop."
Mr Hunt agreed, adding: "The backstop, as it is, is dead ... I don't think tweaking it with a time limit will do the trick, we've got to find a new way."
Simon Hoare, the Tory MP chairman of the Northern Ireland affairs committee, called the comments "worrying and depressing".
"Both of the candidates yesterday moved the goalposts," he told Sky News, adding: "All I can hope is that this is prose caught up in the heat of an election campaign.
"It is not good for the union - this is a very dangerous step that both men seem to have taken."
Dominic Grieve, the Tory Brexit rebel, said the remarks confirmed Brexiteers would simply "put up another obstacle" if anyone was able to solve the backstop issue because it is being "used as an excuse because of this radicalisation".
"When challenged and confronted, he radicalised even further and excluded any possibility of trying to negotiate some way out of the backstop at all. It had to go in its totality," Mr Grieve told a People's Vote event.
"The consequence of that is make it the choices starker and starker.
"I've always been willing as a politician to listen to people willing to come up with credible compromises but what I've found so staggering about the Conservative leadership (contest) is it has been played to a tune of growing extremism."
Speaking alongside Mr Grieve, Labour MP Margaret Beckett called the candidates' backstop pledges "terrifying" and accused them of throwing "the Irish situation under a bus".