Parliament rejected all amendments to the Rwanda bill made by the House of Lords.
The bill, which aims to send some asylum seekers to Rwanda, will return to the upper chamber for further scrutiny on Tuesday.
The government is expected to pass legislation declaring Rwanda safe this week, allowing the bill to override any further amendments made by peers.
The plan to send asylum seekers to Rwanda has faced opposition since it was announced in April 2022 and the UK has reportedly held talks with other countries about replicating the scheme.
On Monday, MPs voted down six amendments to the Rwanda Bill, including one that would have exempted individuals who supported the UK's armed forces overseas from removal.
The government also rejected calls to exempt victims of modern slavery from the Rwanda scheme, instead proposing an annual report on the policy's impact on victims.
The Rwanda Bill will not become law until both Commons and Lords agree on the final wording, a process called parliamentary ping-pong.
The Bill will now return to the Lords, where peers may make additional changes, potentially prolonging the parliamentary disputes.
According to the Times and confirmed by the BBC, internal government documents reveal that
Costa Rica, Ivory Coast, and Armenia have been considered as potential locations for hosting refugee camps similar to the one proposed for Rwanda.
The plans are currently in a "holding pattern," with other countries waiting to see if the Rwanda scheme succeeds before making a move.
The Times also reports that Morocco, Tunisia, Namibia, and Gambia explicitly declined to enter technical discussions about such camps.