The Commons Speaker is facing accusations he played "party politics" by granting a vote on Labour's Gaza ceasefire motion.
Sir Lindsay Hoyle broke with convention to allow the vote during a debate, sparking fury from SNP and Conservative MPs.
He said he allowed the vote on to protect MPs' safety, but it saw the Commons descend into acrimony.
Sir Lindsay later apologised, but still faces calls to resign.
The move meant Labour MPs could call for a ceasefire without backing a differently-worded SNP motion, limiting a potential Labour rebellion.
Health Minister Maria Caulfield claimed the decision was made "under undue pressure" from Labour, and accused Sir Lindsay of "putting party politics" above his obligation as Speaker to be impartial.
This has been denied by both Labour and a source close to the Speaker.
Some 56 Tory and SNP MPs have signed a motion declaring they have no confidence in Sir Lindsay, who is due to meet parties for clear-the-air talks.
The row erupted during a debate allocated to the Scottish National Party, during which they are allowed to put forward motions for debate and vote.
The SNP tabled a motion calling for an "immediate ceasefire" in Gaza and calling for an end to the "collective punishment of the Palestinian people".
Labour, which has shifted its stance on the conflict on recent days, tabled an amendment that also backed an immediate humanitarian ceasefire, but also noted that Israel "cannot be expected to cease fighting if Hamas continues with violence".
Sir Lindsay broke with tradition on such Commons debates by allowing a vote on Labour's amendment to the SNP's motion.
After the Conservatives then said they wouldn't take part, Labour's motion was passed, meaning a standalone vote on the SNP wording couldn't take place.
Explaining his decision, Sir Lindsay said he wanted to give MPs the chance to vote on "the widest range of propositions," and was also concerned about threats to MPs' security over the issue.
But he was accused of allowing the vote to be "hijacked" by Labour, with some SNP and Tory MPs walking out in protest.
Sir Keir suffered a major revolt over Gaza in November when 56 of his MPs, including 10 frontbenchers, defied him to back an SNP motion urging an immediate ceasefire.
In a statement after the debate, SNP Westminster leader Stephen Flynn said Sir Lindsay had "colluded" with Labour leader Sir Keir Starmer to "block Parliament voting on the SNP motion".
Speaking on Thursday, Labour campaign co-ordinator Pat McFadden acknowledged that party leader Sir Keir had lobbied Sir Lindsay before the debate to allow a vote on Labour's motion.
But he denied reports Labour had threatened to withdraw support from the Speaker after the election unless he allowed the vote, adding that Sir Lindsay had acted in "good faith".
He blamed the Conservatives' decision not to take part in the debate for a vote on the SNP's wording not taking place, accusing them of trying to avoid a rebellion from their own MPs.
This was denied by Health Minister Maria Caulfield, who added that Sir Lindsay's decision meant MPs from her party could face criticism for not backing the SNP motion.
"He took the threats to Labour MPs seriously, but took no consideration of what would happen to Conservative MPs," she told BBC Radio 4's Today programme.
There is no formal mechanism allowing MPs to oust the Speaker, but it is a convention they should have the confidence of the main parties in the Commons.
On Thursday more MPs signed an early day motion signed by Tory and SNP MPs expressing no confidence in him.
SNP MP Pete Wishart was one of the MPs to put their names to the motion, and said he had done so because the "position of the Speaker is pretty much untenable".
However, many other MPs said they would not be taking this step.
Former Conservative minister Robert Buckland said he accepted the Speaker's apology and would not be asking for a vote of confidence.
Sir Lindsay was first elected as a Labour MP but after becoming Speaker he relinquished his party affiliation, as is the convention.
Israel launched its operations in Gaza following an attack by Hamas on southern Israel on 7 October, during which about 1,200 people were killed and more than 240 others taken hostage.
Since then, Israel's military campaign has killed more than 29,000 people in Gaza, according to the Palestinian territory's Hamas-run health ministry, whose figures are accepted by the United Nations.