Australian Prime Minister Malcolm Turnbull claimed victory Sunday, eight days after the election.
Malcolm Turnbull has his majority, but he is beset on all sides.
Both Mr Pyne and Resources Minister Josh Frydenberg both emphasised Prime Minister Malcolm Turnbull's mandate on Monday, amid reports conservatives wanted more of a say on policy after the result.
Shorten yesterday called Turnbull to congratulate him and conceded electoral defeat even as the vote counting was underway, according to media reports here.
"We are trustees for the little grandchildren and of course their grandchildren".
Labor, which now has 66 seats under its belt and is expected to win three more, conceded defeat.
"It is vital that this Parliament works", said Mr Turnbull, adding that Australia faced numerous challenges including a rocky transition away from a dependence on mining-driven growth.
"Whoever said that if they did really say it they should put their name to things like that because it sounds very fearless and chest beating when you say it anonymously but I'd love a person who says things like that to actually put their name to it because without their name, it's just cowardice obviously", Mr Pyne told the ABC in response.
Mr Turnbull welcomed the remark, pledging to work not only with the opposition, but with a new host of crossbenchers. "It is vital that we work together and as far as we can ensure that we all agree... consistent with our policies that we took to the election".
The leader, who was returned to the seat of Maribyrnong in Victoria, has hinted that he will bring in a private member's bill to legalise same-sex marriage when parliament returns.
While debate has continued to rage over the future prospect of implementing an online or electronic voting system for future election counting continues in five seats which are determined too close to call. Cowan in Western Australia and Hindmarsh in South Australia are trending to Labor.
But while there will be no change for now, Turnbull is in a weakened position after the poll, having lost his comfortable majority in the House of Representatives and the internal blame games are already taking place.
In his letter to the governor-general, Mr Turnbull told Sir Peter he had the commitment of two independents, Bob Katter and Cathy McGowan, while Andrew Wilkie had indicated he would not support a vote against confidence or supply unless there was a case of illegality.
Hamstrung by conservatives in the coalition, Turnbull was also unable to pursue the more socially progressive agenda that many voters expected of him. "I hope for our nation's sake the Coalition does a good job; I hope they run a good government", he said.
Nick Xenophon has emerged as a powerbroker. There was a one in three chance, S&P warned, that it would downgrade the nation's AAA credit rating by 2018 if the parliament failed to introduce savings or revenue measures that reduced its budget deficit to a "balanced position" by the early 2020s.
He will also have to renegotiate the coalition agreement with the Nationals.
Senator Cory Bernardi, one of the coalition's most vocal right-wingers, called the election "a disaster" and has since made moves to establish his own conservative movement, although he denies plans to defect from the Liberal party.