Sunak has invested huge political capital in the Rwanda scheme before an election later this year he is predicted to lose, saying it will help meet his pledge to stop thousands of people arriving in Britain without permission in small boats.
The House of Lords, upper house of parliament, for a third time sought to make changes to the new legislation after the House of Commons lower house of parliament rejected its second set of proposals on Monday.
But the move is unlikely to stop the legislation from getting approval this week, meaning it will become law. Sunak hopes to start flights to Rwanda as soon as possible, but the scheme might still be challenged in the courts.
The legislation will now return to the House of Commons on Wednesday when Conservative lawmakers are expected to vote against the proposed changes. The upper chamber might then decide it has failed in convincing elected lawmakers to make any changes and decide to pass it.
Under the policy formulated two years ago, any asylum seeker who arrives illegally in Britain will be sent to the East African nation to try to deter dangerous Channel crossings in small boats and smash the people smugglers' business model.
The first planned deportation flight in June 2022 was blocked by the European Court of Human Rights (ECHR), before the UK Supreme Court last year declared the scheme unlawful.
(Reporting by Elizabeth Piper and Alistair Smout; editing by William James)
