Leaving the EU by the end of October is a “hard red line” and will happen in “all circumstances”, Andrea Leadsom has said in her pitch for leadership.
The ex-Commons leader said she had a plan for a “managed exit”, adding that Parliament could “not stop us leaving”.
But her rival Mark Harper said it was “not possible” to leave by 31 October, while Matt Hancock said Brexit could not be solved by “threatening no deal”.
Ten Conservative candidates are in the race to be leader – and next PM.
The deadline for Brexit was pushed back to October after MPs rejected Theresa May’s withdrawal agreement with Brussels three times.
The European Union has repeatedly said the agreement will not be re-opened, with chief negotiator Michel Barnier insisting “a new prime minister will not change the problem.”
What have the leadership contenders said about Brexit?
“In all circumstances we are leaving the European Union on 31 October,” Mrs Leadsom told her official campaign launch. “Our country and our party cannot afford any more indecisiveness.”
The Brexiteer MP set out her plan for what she calls a “managed exit” from the EU, which includes striking a “temporary trade agreement” and a plan to negotiate contingency arrangements with Brussels over the summer recess.
She said these could be discussed at a summit with the new incoming EU commissioners and heads of government in September.
But at his official campaign launch, Mr Harper – an outsider in the race – said it was “not possible or credible” to leave on the terms of a new deal by the existing deadline of 31 October. Renegotiating and getting a deal past MPs would take longer, he said.
He said there could be a majority in the Commons to leave without a deal, but only if ministers demonstrated they had “strained every sinew” to get a new one.
Meanwhile, Health Secretary Mr Hancock – who is also competing for the top job – told BBC Radio 4’s Today programme his plan was “eminently deliverable” by 31 October, as the EU was open to changing the political declaration part of the agreement.
“We need to solve Brexit and we cannot do it by threatening no deal,” he said, adding: “Parliament will not allow a no-deal Brexit to happen.”
Home Secretary Sajid Javid reiterated that although he wanted a revised deal, “if we got to end of October and the choice was between no deal or no Brexit, I’d pick no deal.”
Mr Javid, who launches his campaign on Wednesday, released a campaign video on Tuesday morning. BBC political editor Laura Kuenssberg says it is the first big attempt by a candidate to communicate a personal story, introducing viewers to his family and background.
Meanwhile, he told the Evening Standard he was “very open minded” about having different immigration rules for regions such as London after Brexit, and could scrap Mrs May’s policy that EU migrants should earn at least £30,000 to be considered for admission.