The home secretary has warned the Speaker against changing Commons conventions due to intimidation from outside parliament, telling Sky News: “The only thing MPs should fear is the ballot box.”

James Cleverly offered his support to Sir Lindsay Hoyle to stay in post – despite 68 MPs having now signed a no-confidence petition against him after Wednesday’s chaotic scenes in the Commons – calling him “a breath of fresh air”.

But he added: “We should not be changing our procedures in response to threats or intimidation. That would indicate that the threats and the intimidation is working – that is the opposite of the message that we want to send.

“If people think that they can target members of parliament, they are wrong. The full force of the law will be brought down.”

Politics live: Speaker comes out fighting

A huge row erupted on Wednesday as parliament held an opposition day debate over the Israel-Hamas conflict, with the SNP calling for an immediate ceasefire.

Pressure had been mounting on the Labour Party to move away from the government’s position of calling for a pause in fighting to echo the SNP’s stance – and they announced they would put forward their own amendment, calling for a ceasefire, albeit with a number of caveats.

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Commons conventions say that opposition motions cannot be amended by opposition parties, but Sir Lindsay took the decision to let Labour’s position be debated and voted on, claiming it gave MPs the widest range of positions to discuss and back, and citing the safety of members who were facing threats and intimidation unless they supported calls for a ceasefire.

But his decision was met with rage from the Conservatives, who pulled their own amendment and “played no further part” in the proceedings, and ended with the SNP not even getting to vote on their own motion.

Despite the Speaker making two apologies in the Commons on both Wednesday and Thursday for how his decision had played out, calls for him to resign grew – led by the leader of the SNP, Stephen Flynn, who said his position was now “intolerable”.

Prime Minister Rishi Sunak also criticised Sir Lindsay’s actions, calling them “very concerning”, while former home secretary Suella Braverman wrote an angry piece in the Daily Telegraph, saying it had “undermined the integrity of Parliament” and that “the Islamists, the extremists and the antisemites are in charge now”.

Asked about his position on the Sir Lindsay as the row entered its third day, Mr Cleverly said: “I think the Speaker’s done a fantastic job. I think he’s been a breath of fresh air compared with his predecessor.

“He made a mistake. He apologised for the mistake. My view is that I’m supportive of him.”

But the current home secretary said it would be down to MPs to decide his fate, adding: “The selection of the speaker is House business and for the House of Parliament rather than for government.

“And I know that sounds like we’re dancing on the head of a pin, but in our constitution it’s a very important division. So this is House business for members of parliament, rather than for the government.”

There is no formal way for the Speaker to be removed, but he could choose to resign if calls for him to go continue to grow – as one of his predecessors, Michael Martin, did in 2009.

However, with support from the Labour benches and senior Conservatives, Sir Lindsay could instead decide to fight on to stay on post.

The Tories have sought to blame Labour for the shambolic scenes in parliament this week, amplifying reports that party leader Sir Keir Starmer threatened to withdraw support from the Speaker if he did not select their ceasefire amendment.

A Conservative source told Sky News on Friday: “Starmer’s undermined parliament, bullied the speaker into doing something he admitted was “wrong”, and it sadly won’t be long before more antisemitic views emerge from Labour.”

And Energy Secretary Claire Coutinho told reporters: “I think the speaker is a decent man. He’s a really well respected parliamentarian. I didn’t agree with the ruling that he made, but I think the real culprit here is Keir Starmer.

“I think he’s put the speaker in an intolerable position by saying that we should bow to intimidation and external influences. No intimidation should change the way that we vote in parliament or what we vote on.”

But Sir Keir “categorically” denied making any such threat, telling reporters that when he met Sir Lindsay, he “simply urged” him to have “the broadest possible debate” by putting a number of options in front of MPs.

The Labour leader added: “The tragedy is the SNP walked off the pitch because they wanted to divide the Labour Party and they couldn’t, and the government walked off the pitch because it thought it was going to lose a vote.”

Speaking to Sky News on Friday morning, shadow home secretary Yvette Cooper insisted Sir Lindsay was “right” to select Labour’s amendment to the ceasefire vote – which ended up passing – “making sure the widest possible range of views can be debated, sit on and can be voted on, that is something that is good for democracy”.

But she agreed decisions on parliamentary procedure should not be made because of intimidation from outside.