The LNP have ruled out accepting Billy Gordon's support in any vote in the parliament, while Labor have said they would not deal in "hypotheticals" and instead wanted to give Mr Gordon "time" to decide his own future.

The two Katter MPs, who once again are positioned as potential kingmakers in the Queensland Parliament, said they would work with Mr Gordon on the cross bench, but are yet to decide which way they would swing if the Opposition did force a confidence motion in the government.

Indigenous mayors in Mr Gordon's north Queesland electorate have advoated supporting him until the police investigation into the domestic abuse claims is finalised.

Mr Gordon was due to undergo eye surgery on Monday, but sent out a statement late on Sunday saying he was concerned he was being denied "natural justice" and was seeking legal advice.

Resignation

He resigned from the party on Monday, rather than be sacked, writing about his decision on Facebook.

"This morning I sent this to ALP State Secretary, Evan Moorhead," he wrote just after 2.30pm.

"Dear Evan,

I accept with deep regret that the Premier has determined that I should no longer be a member of the Australian Labor Party. I do not wish the Premier and the party to be put through the pain of expelling me.

On this basis I hereby resign as a member of the Australian Labor Party.

Yours sincerely

Billy Gordon Member for Cook."

Support

Ms Palaszczuk, while calming her rhetoric against Mr Gordon, said a by-election remained her preferred solution, but she would not yet discuss what Labor would do with his vote if he remained on the cross bench.

"I had a conversation with Billy Gordon yesterday [Sunday], he is now of course, extremely distressed," she said.

"Anyone who has been told the things I told him would put you in a state of distress.

"I believe that he should be given time to consider his position in a detailed manner that he can consider by himself and he should take his own counsel. But my resolution remains.

"I hope that he will do the right thing and resign and I want to give him the opportunity to do so.

"I believe he needs time to make his own decision. So I am giving him that time. And I am not dealing with hypotheticals until he has time to deal with those issues on his own."

Legally, Mr Gordon cannot be forced, or induced, to quit parliament. It leaves Labor in the position of potentially having to deal with Mr Gordon voting with them to pass legislation in the minority parliament, having tried to sack him from the party for being dishonest.

Opposition Leader Lawrence Springborg said he had no such qualms.

"If Billy Gordon were to actually remain in Parliament and vote with the LNP on any vote, we would send one of our members out of the chamber, to cancel out his vote," he said.

"Now if Annastacia Palaszczuk and her government are being consistent, they should do similarly. "You cannot on one hand say he is unfit to be in parliament and yet say that you are looking at the possibility of accepting his vote, if he remains as the member of Cook."

"Misled" Parliament

Mr Springborg has continued to attack Ms Palaszczuk on how she handled the allegations she was presented with in an email from Mr Gordon's former partner.

The email contained allegations of missed child support, a failure to lodge tax returns and domestic abuse. Mr Gordon, after speaking to Ms Palaszczuk admitted to the first two in parliament on Friday.

Ms Palaszczuk said the matter had been finalised. But later that day, the allegations of domestic violence were made public by a former LNP MP on a newly launched news website.

Ms Palaszczuk, who said Labor had, through State Secretary Evan Moorhead encouraged the woman to go to the police, then referred the issue for investigation herself.

Mr Springborg said Ms Palaszczuk had "misled" parliament. Ms Palaszczuk said Mr Springborg was being "a wrecker".

"I was completely upfront," she said.

"I know that that Lawrence Springborg wants to continue playing the wrecker in this, but I have been completely upfront, completely transparent and can I just remind everyone, the actions under the former premier Campbell Newman, when he let these issues run its course, did nothing.

"I stood by my integrity principles.

"As soon as my chief of staff raised those issues with me we thought it appropriate it in the first instance for the state secretary top deal with some of those issues contained in the letter.

"Some of those issues were of a private nature and the person concerned was encouraged to go to the police.

"She was encouraged to go to the police.

"Once those issues became public, I was very concerned that the nature of those complaints were in the public domain and I had no other option but to refer those matters to the police for investigation."

The police investigation into the claims is on-going.

Katter's 

In the meantime, Labor has once again been in discussions with the Katter Party.

Given the timing needed for a by-election writ, if Mr Gordon was to resign within the next week, a by-election could be held before the next sitting of parliament.

If he does not, Labor, without the support of the Katter MPs, will be faced with having one less member than is needed for a parliamentary majority.

Robbie Katter and Shane Knuth said they had been speaking with Labor's leadership team during the weekend over what it would take to gain their support.

Both said it was the same as two months ago, when who would lead Queensland first became an issue – which was a 27-point plan, including commitments for an ethanol mandate in fuel and an in-land highway for regional and rural Queensland.

But that doesn't mean the two MPs have given their votes to the LNP. Mr Springborg has not yet committed to bringing a confidence vote against the Palaszczuk Government during the May 5 sitting of parliament, but he hasn't ruled it out either.

"We didn't go the other way [voting against Labor in the confidence motion – they abstained] because we believe that we wanted to give the government the opportunity and a chance to prove themselves," Mr Knuth said.

"So that really is about whether we are going to abstain from a position and this is something we will be discussing with our party."

But if Mr Gordon was to remain in parliament, Mr Katter said the party "certainly don't have any problem working with him".

"He was elected as a member of Parliament, albeit they may not have known about those indiscretions and I am sure he has something to offer and as long as he has something to contribute, we'll be more than happy to work with him on the cross bench," Mr Katter said.

Negotiations are on-going. But so is the waiting game.