Matt Hancock would put his premiership on the line within days of entering Number 10 by putting his Brexit plan to the Commons.
The Tory leadership hopeful said that he would ask MPs to back his Brexit plan in principle “immediately” if he became prime minister.
He claimed the European Union would shift its position and agree to a time limit on the Northern Ireland backstop if the new prime minister could show they had support at Westminster.
“The strength of my position will be the ability to show that the House of Commons, in principle, backs this new arrangement,” he said.
Mr Hancock insisted that no-deal was not an option because the Commons would block it, so the only way to leave the EU was with an agreement.
He told BBC Radio 4’s Today programme: “As prime minister I would propose to put my plan, which I have already published, to the House of Commons, in principle, immediately and therefore show the European Union that this plan is deliverable through the House of Commons.”
He said the EU could agree to the time limit at the October meeting of leaders.
“They nearly proposed a time limit on the backstop before,” he claimed, “but they didn’t think that the Prime Minister, Theresa May, would be able to get it through the House of Commons.”
Mr Hancock’s Brexit plan to find an alternative to the backstop would involve cross-border co-operation with the Government in Dublin and cross-community efforts in Northern Ireland.
An initial find of up to £1 billion would be spent on supporting the border community and putting the technology and administration in place to keep the border open.
His plan calls for a “national mission” to make the technology for alternative arrangements to a hard border work.
In a message to leading rival Boris Johnson, Matt Hancock said “the front-runner has never won before”.
Mr Johnson has steered clear of radio and TV studios so far in the campaign, and Mr Hancock said: “I certainly think that everybody who puts their name forward to be prime minister should be open to scrutiny, should be accountable, should come on the Today programme and on other broadcast programmes.
“I think everybody should participate in the proposed TV debates and I think we have got to ask the question, why not?”
He said the candidates should “come and be scrutinised because that is the best way to ensure that we get the best next prime minister”.