Sir Keir Starmer could face an investigation from the privileges committee for allegedly pressuring Lindsay Hoyle to allow a Labour amendment ahead of last week's vote on a ceasefire in Gaza.
The Labour leader has "categorically" denied threatening the Speaker, saying he "simply urged him to ensure that we have the broadest possible debate".
Commons Leader Penny Mordaunt accused him of being a "bully and a cheat" when it came to last week's debate.
Ministers are said to have held talks yesterday about tabling a motion seeking to refer Starmer to the cross-party privileges committee to investigate the allegations, with sources telling the Times Mordaunt believes Starmer's behaviour was a "breach of privilege".
Sir Keir Starmer could face an investigation from the privileges committee for allegedly pressuring Lindsay Hoyle to allow a Labour amendment ahead of last week's vote on a ceasefire in Gaza
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Some SNP MPs are said to support an investigation, too.
Hoyle sparked the fury of Tory and SNP MPs after he broke precedent by selecting a Labour amendment, along with a Government amendment, to an Opposition Day motion calling for a ceasefire in Gaza. Protocol dictates that the Commons Speaker would only select one of the amendments and it is highly unusual for an opposition amendment to be selected.
He apologised to the House of Commons following a walkout by SNP and Tory MPs, saying it was never his “intent” for the Gaza debate to have descended into such mayhem.
There were suggestions that Starmer had pressured Hoyle into selecting the Labour amendment in order to avoid another rebellion from his own MPs.
In order for the privileges committee to begin an enquiry, an MP must apply to the Speaker to approve a debate and vote in the Commons. The Speaker often makes such a decision with advice from deputies and clerks.
Addressing the Commons in the wake of the chaotic debate, Mordaunt said: "This house will never bow to extremists, threats or intimidation. It has not, it will not, it must not.
"And I would ask all Honourable members not to do this house a further disservice by suggesting that the shameful events that took place yesterday were anything other than party politics on behalf of the Labour Party."
The Leader of the House of Commons continued: "Let me bring the house up to date. Firstly, it fell to the Government benches to defend the rights of a minority party in this House.
"If the honourable lady opposite cannot bring herself to reflect on the appalling consequences of her party's actions yesterday, if she cannot rise above the narrow and immediate needs of her weak and fickle leader, to fulfil her duties to this house as its shadow leader, perhaps she might like to reflect on the damage her party has done to the office of the Speaker.
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There were suggestions that Starmer had pressured Hoyle into selecting the Labour amendment in order to avoid another rebellion from his own MPs
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"I would never have done to him what the Labour Party have done to him.
"Secondly, we have seen into the heart of Labour's leadership. Nothing is more important than the interests of the Labour Party."
Hoyle is also under fire for his role in selecting the Labour amendment, with 79 MPs having now signed an early day motion saying they have no confidence in the Commons Speaker - an increase of eight MPs just yesterday.
While the Government is not currently pushing for him to go, if the number of backbenchers signing the no confidence motion continues to rise it will raise fresh questions about the Speaker's ability to carry on in the role.