Boris Johnson's claim that world trade rules could be used after Brexit to avoid tariffs "isn't true", cabinet minister Liam Fox has said.
The international trade secretary, who is backing Jeremy Hunt for leader, said the EU will apply trade tariffs.
Mr Fox, a Brexiteer, said he would prefer to leave with a deal and Mr Hunt has a "good chance" of getting one.
Tory MP Liz Truss, who is backing Mr Johnson, said not leaving the EU on 31 October would be a "disaster".
It has been three years since the UK voted to leave the EU in a referendum.
Speaking to the BBC's Andrew Marr Show, Mr Fox rejected Mr Johnson's claim that the UK could secure a 10-year standstill in current arrangements using an article of the EU's General Agreement on Tariffs and Trade .
"It isn't true, that's the problem," he said.
Mr Fox said Mr Johnson's argument that a new free trade agreement could be negotiated during an implementation period "doesn't actually hold".
"If you don't get the withdrawal agreement through Parliament, there is no implementation period during which we can do anything at all," he said.
"Secondly, if we leave the European Union without a deal the EU will apply tariffs to the UK because you can only have exemptions, as described, if you already have a trade agreement to go to.
"Clearly if we leave without a deal it's self-evident we don't have that agreement, so Article 24 doesn't hold in that circumstance."
But he said a no-deal Brexit is the "legal default position" and the UK will have "no negotiating capital" if it is ruled out.
Justice Secretary David Gauke, who had been backing Rory Stewart for leader until the international development secretary's elimination, also criticised Mr Johnson's Brexit plan, saying it was not "credible".
And Scottish First Minister Nicola Sturgeon told Sky News's Sophy Ridge on Sunday that choosing Mr Johnson as prime minister would be "disastrous" for the Conservatives, particularly in Scotland - which voted to remain in the EU.
When asked what she thought of SNP Westminster leader Ian Blackford's comments during PMQs last week that Mr Johnson was a "racist", she said: "I agree with Ian Blackford's comments."
She said Mr Johnson has "made overtly racist comments" during his career.
But also speaking on Sky News, Conservative MP Rishi Sunak, who is backing Mr Johnson, defended the leadership hopeful.
He said Mr Johnson was not racist and has "apologised for any offence caused" by his comments over the years.
Elsewhere, Chief Secretary to the Treasury Liz Truss, told BBC 5 Live's Pienaar Politics that Brexit was a matter for the executive and not for Parliament - which rejected Theresa May's Brexit deal three times.
She also criticised Mr Hunt, accusing him of "kicking the can down the road" on Brexit, which "would be a disaster".
She said Mr Johnson would seek to re-negotiate with the EU and would be "much clearer that we are prepared to leave on 31 October".
Mr Hunt has said he would delay leaving on 31 October only if a potential deal with the EU was in the pipeline.
While Mr Johnson has been more outspoken on the subject, Mr Fox said he had not heard Mr Johnson say he would definitely leave on 31 October, even if a new deal was within reach.
The EU has repeatedly said the withdrawal agreement will not be renegotiated.