Rishi Sunak has pleaded with Tory MPs to back his Rwanda plan as Home Secretary James Cleverly admitted it pushed the envelope of international law.

The Prime Minister was involved in intensive efforts to persuade would-be rebels to back the legislation in a crunch Commons vote on Tuesday night – holding crisis meetings with the various factions in the Conservative Party as MPs considered their positions.

But as hardliners on the Tory right pushed for changes to toughen up the legislation by blocking interference from foreign courts, Mr Cleverly suggested the legislation was already close to the limits of what would be possible.

The Rwandan government has threatened to pull the plug on the deal if it breaches international law.

Would-be rebels have warned Mr Sunak that “major surgery” is still required to fix the flagship asylum legislation, with dozens of Conservatives thought to be prepared to either abstain or vote against it.

Read more: Sunak scrambles to hold onto authority over troubled Rwanda Bill

A revolt by 29 Conservative MPs could be enough to defeat the Safety of Rwanda Bill at its first Commons hurdle – something that has not happened to a piece of government legislation since 1986.

In a social media post, Mr Sunak publicly pleaded with MPs to support him, saying: “To stop the boats, we need to back this Bill.”

In the Commons, Mr Cleverly said: “The actions that we are taking, whilst novel, whilst very much pushing at the edge of the envelope, are within the framework of international law.”

He added: “The Prime Minister has been crystal clear that he, and the Government that he leads, will not let foreign courts destroy this Rwanda plan and curtail our efforts to break the business model of those evil people-smuggling gangs.”

It was actually the UK Supreme Court which scuppered the plan to send some asylum seekers who cross the English Channel to Rwanda rather than allowing them to attempt to stay in the UK.

The court ruled against the scheme, but the new legislation and a treaty with Rwanda are intended to make it legally watertight.

Read more: Rishi Sunak's Rwanda plans risks angering Tory right over ECHR powers

But groups on the Tory right want it to go further, potentially overriding the European Convention on Human Rights to remove the possibility of Strasbourg judges blocking the removal of people to Rwanda.

The New Conservatives, made up mainly of MPs elected since the 2016 Brexit referendum, are one of the main Tory factions with reservations about the plan and representatives were invited to a breakfast meeting with Mr Sunak in Downing Street as he sought to win them round.

But Jonathan Gullis, one of those who attended the breakfast summit, told TalkTV he still had “grave concerns” about the legislation and had not yet decided how he would vote.

“I still have those concerns that we will end up being bogged down with individual claims that mean that we’ll see very few people put on the plane to Rwanda,” he said.

The European Research Group (ERG), another prominent caucus on the Tory right, claimed it had enough MPs to scupper the Bill.

Deputy ERG chairman David Jones told Times Radio: “We believe we have the numbers, if necessary, to stop the Bill progressing.”

The ERG and allies will meet again on Tuesday afternoon in Westminster, just hours before the vote, to decide how to respond.

The New Conservatives’ invitation to Downing Street follows a meeting in Danny Kruger’s office on Monday night – attended by former immigration minister Robert Jenrick and former home secretary Suella Braverman – which concluded the Bill “needs major surgery or replacement”.

Mr Jenrick used his Commons speech to push for stricter curbs on a migrant’s ability to legally challenge their removal and for the ability to overrule European Court of Human Rights injunctions.

Read more: Immigration minister Robert Jenrick quits over Sunak's Rwanda plan

He told MPs: “This Bill could be so much better. Let’s make it better.”

Allies said Mr Jenrick is minded to vote against the Bill unless the Government is prepared to make the necessary changes.

One Conservative MP said Mr Jenrick, who quit as a minister over the legislation, would play an influential role in the decision on how to vote.

The MP, who attended the breakfast meeting in No 10, told reporters the Prime Minister had said he would listen to ideas for “tightening” the Bill but did not commit to specific amendments.

He said: “I would love to know what he means by ‘tightening’ the Bill.”

The MP added that backbenchers were “falsely” pinning their hopes on the possibility of amending the Bill, and were “deluding themselves” if they believed they could vote it down at a later stage.

A No 10 source said: “The tests set for the Bill have been met and we will continue to listen to and engage with colleagues across the party as it passes through Parliament. This Bill will work and will do what we need it to do.”

Former Cabinet minister Sir Simon Clarke joined the chorus of criticism of the Bill, saying the Government should “withdraw the legislation and come back with a new Bill” that could avoid appeals against being sent to Rwanda.

He said: “This is a matter of practical politics as well as principle; we have failed to deliver on our promise to stop the boats twice already. There is neither public patience nor sufficient time for us to fail again.”

One Nation moderates – numbering around 100 MPs – said they will recommend backing the Bill, but the group is likely to resist any amendments that would risk the UK breaching the rule of law and its international obligations.

Mr Sunak was due to meet the One Nation group to calm their nerves on Tuesday afternoon.

The Bill allows ministers to disapply the Human Rights Act but does not go as far as overriding the European Convention on Human Rights, which Tory hardliners have demanded.

Labour leader Sir Keir Starmer dismissed the Rwanda plan as a “gimmick” and piece of political “performance art”.