Theresa May has called on opposition parties to work with the Government on issues such as counter-terrorism, workers' rights and Brexit.
And she put the spotlight on Jeremy Corbyn as she said that all party leaders should condemn the bullying and harassment which some candidates in last month's general election suffered.
The Prime Minister's call came ahead of a major speech on Tuesday, at which she is expected to urge other parties to "come forward with your own views and ideas" to help the Government debate key issues and find a "better way forward".
First Secretary of State Damian Green, who is effectively the PM's deputy, said that Mrs May's initiative, to be launched alongside the publication of a report by former Tony Blair aide Matthew Taylor on the gig economy, represented "a grown-up way of doing politics".
Mr Green told BBC Radio 4's Today programme the public would welcome a move away from politics in which parties "just sit in the trenches and shell each other".
But Labour's shadow communities secretary Andrew Gwynne said the PM had "finally come clean and accepted the Government has completely run out of ideas" and was having to "beg for policy proposals from Labour".
"No one will be fooled," said Mr Gwynne. "The Tories are the party of the privileged few. This is further evidence that this Government can no longer run the country."
Liberal Democrat spokesman Tom Brake said Mr Corbyn was already supporting Mrs May's "hard Brexit" plans, adding: "A call for Labour to contribute is superfluous. On the single biggest issue of our generation - Brexit - Corbyn isn't contributing, he is cheer-leading."
Asked what topics she would like to work with other parties on, Mrs May told a Downing Street press conference: "The Government has got an ambitious agenda... to address the big challenges that the country faces. Of course, one of those is getting the Brexit negotiations right, but there are other challenges we face as a country too.
"I think the public will rightly want us to get the broadest possible consensus in looking at those issues."
She highlighted the workplace rights which will be discussed by the Taylor Report as a possible area for co-operation, as well as moves to prevent the abuse of election candidates.
"Who would not want to work to ensure that workers had the best possible rights and protections in the workplace as it changes?" she asked. "Who would not want to work with us to ensure that we've got the right counter-terrorism powers and capabilities in place?
"And then there's ... this whole question of the abuse and bullying and harassment that people suffered through the general election.
"A number of MPs have clearly identified that that has happened to them, (Labour MP) Yvette Cooper has been clear it is something we need to address. I think we should be working together to ... make sure that the message goes out very clearly that that has no role in our democracy."
Asked whether Mr Corbyn was doing enough in response to complaints of intimidation, Mrs May said: "On the issue of the bullying and harassment of candidates and MPs, I call on all party leaders to condemn that. There is no place for that activity in our democracy and I'm surprised at any party leader who's not willing to condemn that."
Mrs May will use her speech 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".
The address is being seen as an attempt to relaunch her premiership after the humiliation of the election result and amid concerns that the Repeal Bill to enact Brexit may be vulnerable to backbench rebellions.
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: 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."
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.
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."