Theresa May's call for Jeremy Corbyn's Labour and other parties to help "clarify and improve" Government policies represents a "grown-up" way of doing politics, her most senior minister has said.
First Secretary of State Damian Green said the public would welcome a move away from politics in which parties "just sit in the trenches and shell each other".
It comes with the embattled Prime Minister set to acknowledge that the loss of her Commons majority means she has to adopt a different approach to governing, signalling she is prepared to "debate and discuss" ideas with her opponents.
With the Repeal Bill expected to be published this week, Mrs May's overture to opponents will be viewed as an attempt to secure Labour backing for Brexit legislation following signs that pro-EU MPs on her benches will oppose elements of her strategy.
Ahead of the PM's speech on Tuesday, Mr Green said her intervention was not just about Brexit.
He told BBC Radio 4's Today programme: "We're saying that politicians of all parties, it's not just addressed to Jeremy Corbyn, but that there are big issues facing this country, obviously Brexit is the overwhelming one, but there's counter-terrorism, there's workers' rights - the thing that's very much in the news today with the Matthew Taylor report - issues like the industrial strategy.
"And politicians of all parties are invited to contribute their ideas and that's a grown-up way of doing politics.
"I think a lot of your listeners would think actually if politicians just said why don't we do this about a particular national issue rather than just sit in the trenches and shell each other, then we might actually have better government and that's what the Prime Minister is talking about tomorrow."
Mrs May's speech on Tuesday is being seen as an attempt to relaunch her premiership after the humiliation of the election result and the need to strike a deal with the Democratic Unionist Party to prop up her administration in the Commons.
It comes after weekend reports of a plot to oust her by allies of Brexit Secretary David Davis.
Former chief whip Andrew Mitchell, who ran Mr Davis's unsuccessful 2005 leadership bid, sought to play down claims he told a private dinner that the PM had "lost her authority" and was "dead in the water", saying the account of the gathering was "overheated".
Mr Green rejected suggestions Mrs May could be challenged.
He told Sky News: "I'm saying that there is no credible plot going on. There is nothing like that going on.
"The Prime Minister is determined to carry on to lead the party and the country for many years to come and the overwhelming majority of Conservative MPs are behind her in that."
Mrs May will use her speech, at the publication of a Government review of the "gig economy", to return to her core message from when she succeeded David Cameron - a "commitment to greater fairness" and tackling "injustice and vested interests" in recognition that the EU referendum result was a "profound call for change across our country".
Mr Green said Mrs May is convinced she must stay on as PM because the Tories won the most votes and seats at the election, and insisted the "fire burns within her" to change the country as strongly as it did when she took the top job a year ago.
He told Today: "It is her duty and she still has the same ambitions for this country as she had a year ago and she's determined to put them into practice for the good of this country, that's what drives her."
He added: "She thinks not just that it's her duty but that she has a programme for Britain that encompasses not just a good Brexit deal but also a domestic agenda that will spread prosperity around this country, make this a fairer society, tackle some of the injustices that we still have in our society, and that fire burns within her as strongly as ever."
In her speech, Mrs May will insist the fragile position of her Government in the Commons will not stop it being "bold".
But she will accept that the General Election result changes the way she has to work in Parliament.
"In this new context, it will be even more important to make the case for our policies and our values, and to win the battle of ideas both in Parliament as well as in the country," she will say.
"So I say to the other parties in the House of Commons ... come forward with your own views and ideas about how we can tackle these challenges as a country.
"We may not agree on everything, but through debate and discussion - the hallmarks of our parliamentary democracy - ideas can be clarified and improved and a better way forward found."
Shadow communities secretary Andrew Gwynne said: "Theresa May has finally come clean and accepted the Government has completely run out of ideas. As a result they're having to beg for policy proposals from Labour.
"They're also brazenly borrowing Labour's campaign slogans. But no-one will be fooled - the Tories are the party of the privileged few.
"This is further evidence that this Government can no longer run the country."
The Liberal Democrats said Mr Corbyn was already supporting Mrs May's "hard Brexit" plans.
Lib Dem Brexit spokesman Tom Brake said: "A call for Labour to contribute is superfluous. On the single biggest issue of our generation, Brexit, Corbyn isn't contributing, he is cheerleading."
Scottish Government Brexit minister Michael Russell said: "If the Prime Minister is genuinely interested in creating a consensus then Scotland should have a seat at the negotiations to leave the EU."
On Monday, Mrs May will welcome her Australian counterpart Malcolm Turnbull to Downing Street for talks expected to focus on security and defence co-operation, including on counter-terrorism, and trade and investment.
It will be Mr Turnbull's first official visit to the UK as prime minister and will include an audience with the Queen and meetings with other ministers.
But he is no stranger to the UK - or to the Prime Minister - after studying at Oxford University at the same time as Mrs May.