Liam Fox has told Sky News it would be bad for the UK if the country failed to secure a Brexit deal with the European Union.
But speaking to Sky's Sophy Ridge On Sunday, the International Trade Secretary argued it would also damage Europe and so was "not in anybody's interest".
His comments were at odds with those of Foreign Secretary Boris Johnson, who insisted Britain would be "perfectly OK" if it was unable to reach an agreement and that it would not be "apocalyptic".
However, Mr Johnson said the suggestion the UK could leave with no deal was "excessively pessimistic" and that coming to an agreement was "very likely".
He was responding to a warning by the influential cross-party Commons foreign affairs committee, which said there was real possibility the negotiations could end without a deal but had seen no sign of serious contingency planning by Government.
It said failing to prepare for such a scenario would be a "serious dereliction of duty", but Brexit Secretary David Davis has insisted contingency plans were being drawn up.
The Prime Minister has repeatedly said she would rather walk away without a settlement than agree to a "bad deal".
The Brexit Bill is expected to clear its final parliamentary hurdle this week, paving the way for Theresa May to start formal Article 50 divorce proceedings from Brussels.
Dr Fox told Sky's Sophy Ridge: "Your substantive point about not having a deal of course would be bad. But it's not just bad for the UK, it's bad for Europe as a whole.
"That's not in anybody's interest, which is why I understand we need to plan for no deal, but I think it's unlikely to happen because economic reality will get in the way."
He added: "We accept that we are not staying in the single market and there is a price to be paid for not staying in the single market. It's a political decision."
Speaking at around the same time on ITV's Peston On Sunday, Mr Johnson accused the select committee of being "excessively pessimistic" and added: "I think we've got every prospect of doing a very good deal between now and the end of the negotiating period in 2019."
He went on: "I think that actually, as it happens, we would be perfectly OK if we weren't able to get an agreement, but I'm sure that we will.
"I don't think that the consequences of no deal are by any means as apocalyptic as some people like to pretend, and actually what we have seen in the Budget from Philip Hammond last week are preparations for Britain over the next few years."
Mr Davis told BBC One's The Andrew Marr Show he had briefed the Cabinet on contingency plans.
"The aim is to get a good outcome and I'm confident I'll get a good outcome.
"One of the reasons we don't talk about the contingency plan too much is we don't want people to think this is what we are trying to do."
Foreign affairs select committee chairman Crispin Blunt, himself a Tory Brexiteer, told Sky News: "We need a deal. It is in the interests of the United Kingdom to have a deal on leaving the European Union.
"However, if we get to the place where there is no agreement - we can cope with that, but we need to prepare to cope with it.
"And that's why we need to prepare for the implications of no deal and businesses and individuals need to understand the consequences for themselves, the Government certainly needs to understand the implications and they need to do that work now and they need to take public with them."
Speaking to Sky News, shadow Brexit secretary Sir Keir Starmer warned crashing out of the EU without a deal would be "a disaster".
"We absolutely have to have a vote in Parliament before that could possibly happen," he added.