Sunak is facing the biggest challenge to his year-long tenure as he tries to stop MPs on the Conservative Party's right wing from rebelling over their demand that Britain should quit international treaties to set its own migration policy.
His immigration minister quit on Wednesday and he is facing questions as to whether he can get his key policy through a vote in parliament. Some Conservative MPs said on Thursday that Sunak could face a leadership challenge.
At a press conference in Downing Street, Sunak said if the government went any further in disregarding human rights law in the legislation, Rwanda would abandon the deal.
"It is the only approach because going any further, that difference is an inch, but going any further means that Rwanda will collapse the scheme and then we will have nowhere to send anyone to and that is not a way to get this going," he said.
"What everyone should do is support this bill."
The draft legislation comes three weeks after Britain's Supreme Court ruled that Rwanda was not a safe place to send those arriving in small boats on the southern coast of England, and that the plan would breach British and international law.
Britain's Supreme Court ruled Rwanda was not a safe place to send those arriving in boats. (AP PHOTO)
The Rwanda scheme is at the centre of the government's strategy to stop illegal migration. The court's decision was a setback for Sunak who is struggling to revive a weak economy and is heavily trailing the main opposition party ahead of an election expected next year.
Sunak could make the vote in parliament on the new legislation next week a confidence vote - meaning that if he loses, it could trigger a national election - in an attempt to shore up party support.
So far only one Conservative MP has publicly called for a no confidence vote, but she said six of her colleagues have done so privately.
To trigger a leadership challenge, 53 of the 350 Conservative MPs in parliament must write letters of no confidence to the chairman of the 1922 Committee.
Sunak suffered his first parliamentary defeat this week as members of parliament voted to establish a compensatory body for victims of the infected blood scandal.
He named two new immigration ministers on Thursday.
Michael Tomlinson, previously a deputy chairman of an influential group of right-wing MPs, was appointed as the new minister for illegal migration, while Tom Pursglove was named as the minister for legal migration.
A poll last month showed immigration was one of the three biggest issues facing Britain. Only the economy and National Health Service were seen as more important.
Last year net legal migration hit a record of 745,000 people and around 45,000 arrived illegally.
Rwanda currently only has the capacity to accept a few hundred migrants from Britain, but ministers say the plan will act as a vital deterrent to discourage people from making the crossings.
The new bill will instruct judges to ignore some sections of the Human Rights Act (HRA) and provisions of domestic or international law that might deem that Rwanda was not a safe destination, though appeals by people based on specific circumstances would still be permitted.
The former interior minister Suella Braverman, former immigration minister Robert Jenrick and their allies say that does not go far enough, with some wanting Britain to leave the European Convention on Human Rights altogether.
"I'm very concerned that the bill on the table will allow a merry-go-round of legal claims and litigation," Braverman told BBC radio, but said no one was talking about changing the party's leader.
"The reality is, and the solid truth is, that it won't work and it will not stop the boats."
