The Morrison government has waved through a motion in support of a new federal anti-corruption body to avoid an embarrassing defeat on the floor of the House of Representatives on day one of minority government.

The issue was forced by the lower-house crossbenchers, with a Senate motion coming to the House of Representatives for concurrence on Monday, and with the Victorian independent Cathy McGowan bringing forward a private member’s bill to create an anti-corruption body.

With some government MPs signalling internally they would support the motion, the government allowed it to pass on the voices.

But the attorney general, Christian Porter, said the McGowan bill had substantial problems, citing a scenario where the ABC political journalist Andrew Probyn would be the subject of a corruption finding.

Porter told the House that Probyn, a public servant courtesy of his employment at the ABC, had been found by the Australian Communications and Media Authority to have breached the code of the national broadcaster with commentary about the former prime minister Tony Abbott that breached the impartiality standard.

“Under this bill before the House, no ifs ands or buts, Andrew Probyn would be found to have committed corruption,” Porter told the chamber. With MPs interjecting and laughing, Porter stood his ground. “Read the bill,” he said.

McGowan said she respected the expertise of the attorney general, a former prosecutor, but she said if there were problems with her bill, it was incumbent on the government to work with the crossbench to fix them, rather than wave through a concurrence motion for tactical reasons, then refuse to cooperate.

She challenged Porter in the chamber, noting there was now a working majority on the floor of the House for an anti-corruption watchdog. “What will you do to help us to make this legislation better?”

McGowan noted that government backbenchers were in favour of taking action. She said she hoped “from the bottom of my heart” that the government would produce a workable proposition before the end of the week.

She said that, when it came to improving trust in institutions, “what the Australian people want from us is to work together on an issue that matters to them”.

Labor has been pushing a corruption watchdog since January, and the Coalition initially telegraphed some interest, but Porter said in May that there was there was no “persuasive evidence” that current methods of tackling corruption were insufficient.

The issue has been reignited now the Morrison government has lost its majority in the lower house, with crossbenchers insisting the issue be addressed.

On Sunday, dozens of former judges heaped pressure on the government in an open letter, warning that existing anti-corruption agencies were insufficient and a new body was needed to improve trust in public institutions.

The Greens MP Adam Bandt noted in Monday’s debate “we are now in a power-sharing minority parliament” and a number of crossbenchers implored the government, as the Centre Alliance MP Rebekha Sharkie put it, to “lead from the front”.