Andrea Leadsom has pleaded for unity on Brexit amid claims Cabinet ministers want Theresa May to ease up on her "red lines" and with the minority Government already facing pressure in the House of Commons.
The Commons Leader said ministers would "listen and consult" and be "open and responsive" to MPs and peers in a two-year Parliament set to be dominated by Britain's exit from the European Union.
But she also called on parliamentarians to work together "wherever possible" in the national interest.
It comes amid claims of Cabinet splits over Brexit, with Brexit Secretary David Davis's former chief of staff James Chapman claiming the Prime Minister's insistence on leaving the jurisdiction of the European Court of Justice (ECJ) had "hamstrung" his former boss in negotiations.
Mr Chapman also claimed the likes of Mr Davis and Boris Johnson could welcome an easing of the PM's Brexit "red lines", including on leaving the ECJ and Euratom (European Atomic Energy Community), and potential on immigration.
It also follows a Government concession on the Queen's Speech, with ministers pledging that women from Northern Ireland could have free abortions in England after an amendment from Labour MP Stella Creasy apparently gathered support from several Tory MPs.
It highlighted the vulnerability of the Government, which is relying on the support of the Democratic Unionist Party's 10 MPs to get its business through the House of Commons, after the Tories lost their majority in a disastrous general election.
Ms Leadsom, a leading Leave campaigner who has caused controversy with calls for broadcasters to be "patriotic" over Brexit, said MPs and peers must prepare to leave the EU "in a way that brings the country together".
Writing for the Telegraph, she went on: "Government ministers will listen and consult, doing our best to be open and responsive to Parliament.
"Equally, we hope parliamentarians can set aside partisan politics to work together wherever possible in the best interests of our country.
"Such a co-operative approach is easiest when there is already a degree of consensus, yet it matters most on the many issues where there are real disagreements.
"We can of course rely on politicians of all colours to keep challenging the Government whenever they take a different view.
"The great clamour of discussion and debate is what makes our democracy so admired the world over.
"Yet by channelling our collective energies towards a single endpoint, and by coming together to improve our country, we can show British voters that there is more to our politics than just pessimistic bickering."
Her comments follow widespread calls for a cross-party approach to Brexit, reiterated on Saturday by Liberal Democrat spokesman Tom Brake.
"When David Davis' ex-chief of staff is telling you your approach to Brexit is too inflexible, it might be time to think again," he said.
"Theresa May has tied herself up in knots by setting so many red lines so early on in the negotiations.
"We need a cross-party Joint Cabinet Committee on Brexit to provide scrutiny and consensus in the national interest as we navigate these vital negotiations."