Ten amendments in all were presented to MPs, but the Conservatives voted against each one.
Additionally, they want the evidence on Rwanda’s safety to be taken into consideration by lawmakers and judges, something that the new law forbids.
Another proposed modification would shield former members of the British military forces from deportation to Rwanda in the event that they entered the country without authorization.
Before voting started, the Commons discussed the modifications for about four hours. Sir Keir Starmer and Rishi Sunak were present when divisions started.
Speaking in favor of the changes suggested by the upper house were members of the opposing benches.
Stephen Kinnock, Labour’s shadow minister for the Home Office, stated: “They each serve to make this shambolic mess of a Bill marginally less absurd, and as I will come to in a second, they would serve only to put into statute what ministers have actually promised from that despatch box.”