In a joint letter, the Greens and independent MPs and senators say they want a commission to be set up properly after “good faith” consultations with the government in the preceding months.

“We won’t delay the process for political games or point scoring, but won’t be rushed to vote in favour of a bill that doesn’t make the grade,’ the letter signed by 15 parliamentarians reads.

The crossbenchers have called for stronger whistleblower protections, oversight mechanisms, a sturdy budget and the inclusion of third parties seeking to influence government decisions.

“We are united in a will for a better standard of politics, and an integrity watchdog that will be respected by the public and improve trust in our democracy,” the letter says.

“It is now up to the government to deliver an anti-corruption commission that is independent, strong and trusted by the Australian people.”

Asked if the government would accept support from the opposition in exchange for excluding public hearings from the model, Treasurer Jim Chalmers said the form of the commission would be settled by parliament.

“It makes no sense that there’s been this hole in the commonwealth’s armoury when it comes to making sure that the decisions taken in Canberra are above board,” he told the ABC.

“We’ll settle the model with the parliament and we’ll move forward.”

Signatories include Greens leader Adam Bandt, teal independents, Bob Katter, Helen Haines, Andrew Wilkie, Rebekha Sharkie, Dai Le and Senator David Pocock.

The government will bring forward its anti-corruption commission bill in the House of Representatives after it goes to caucus on Tuesday.

The bill is expected to be examined by a committee of MPs and senators.

The government hopes to have the legislation passed this year but it could be pushed into next year if it’s held up in Senate and committee processes.

The opposition says while it’s supportive of a federal anti-corruption commission, it won’t be tied to Labor’s model.

Opposition finance spokeswoman Jane Hume warned of “dire consequences” if the wrong approach is taken.

“Will there be procedural fairness and natural justice? Will hearings be in public or private? When will they be one or the other?” she said on Sunday.

“Because what we’ve seen in other states and other jurisdictions is when a (corruption commission) goes wrong, it actually affects people’s reputations … people have taken their lives.”