The Victorian independent MP Cathy McGowan says she won’t support a no confidence motion against the government while the Wentworth byelection is in play, throwing Scott Morrison a lifeline as he struggles to settle the Coalition after a fortnight of open warfare.

McGowan has not given any permanent undertakings to the government, saying on Wednesday her commitment covered the period of the byelection. “Now is not the time for further disruption,” the crossbencher said.

The government’s position once parliament resumes in September is fraught, given that it holds power by one seat in the House of Representatives. Labor will not grant the government a pair while it is a number down courtesy of Malcolm Turnbull’s departure from parliament.

Turnbull formally farewelled his constituents on Wednesday. In a constituent letter posted on Facebook, he said: “I don’t want to dwell on recent shocking and shameful events – a malevolent and pointless week of madness that disgraced our parliament and appalled our nation.”

The former prime minister issued a final rebuke to Tony Abbott, noting he had always argued that “the best place for former PMs is out of the parliament, and recent events amply demonstrate why”.

Morrison, who has been meeting colleagues since the swearing in of his new ministry before a visit to Jakarta this week, told reporters on Wednesday that as well as securing comfort from McGowan, he had secured a similar verbal assurance from the Queenslander Bob Katter.

The prime minister has been attempting to project a sense of forward motion but a decision by the Victorian Liberal MP Julia Banks to leave politics at the next federal election underscores the reality – that internal tensions remain raw.

Banks confirmed her intentions in a frankly worded statement accusing unnamed colleagues of “bullying and intimidation” during the leadership battle. Reaction was mixed. Female colleagues praised her bravery while conservatives suggested she had done the wrong thing by the party.

Kelly O’Dwyer, the minister for women, said she “deeply regrets” Banks’ decision and “the circumstances that have led to her decision to leave politics”.

“Bullying in any workplace, whether on the shopfloor, or in our nation’s parliament, is totally unacceptable,” she said.

The Liberal senator Linda Reynolds – who also called out her colleagues’ unacceptable behaviour last week – told Guardian Australia she respected Banks’ “integrity and bravery”.

Morrison told reporters he had “no truck with bullying or intimidation” in any form but was vague about how the government would handle the MP for Chisholm’s allegations.

He said the “dramatic events” of last week’s leadership spill had “taken a pretty high human toll inside the parliament”.

“It is a very robust discussion and I know Julia [Banks] has been very concerned about that and she has raised those concerns with me,” he said.

Morrison said he had discussed the matter with O’Dwyer but when asked what action he was taking the prime minister said he was “supporting Julia” and would consult with colleagues to ensure “there can be no question about the culture of the Liberal party”.

“There should not be – and certainly under my authority there would have been – absolutely nothing of that sort taking place.”

Asked about claims that Banks had identified three Liberal MPs as culprits of the alleged bullying in conversations with colleagues, Morrison replied that “those allegations have not been made”, adding: “I act on facts, not on allegations.”

.@jekearsley has confirmed senior Liberals were told @juliabanksmp felt bullied by “a pact of three Liberal MPs” and @9NewsAUS has been given their names. All three have been given a chance to respond before we name them. #auspol — Chris Uhlmann (@CUhlmann) August 29, 2018

All three Liberal MPs named to @NineNewsAUS as having been involved in bullying and intimidating @juliabanksMP categorically deny the allegations. #auspol — Chris Uhlmann (@CUhlmann) August 29, 2018

The conservative MP Craig Kelly told Sky News he thought Banks had “done the wrong thing” – and he advised her to “roll with the punches”.

He said Banks owed an obligation to the party to defend her seat in Melbourne’s east: “The party gives you the opportunity to run, you owe the party that back to recontest the seat.”

Kelly said the leadership challenge had been “a very testing and trying time for everyone” and expressed hope that Banks would reconsider.