The government has suffered five defeats in the House of Lords over its bill to revive its proposed Rwanda deportation scheme.
The legislation would deem Rwanda a safe country to send asylum seekers to, in a bid to stop removals being derailed by appeals.
But peers backed changes to make it easier for judges to challenge this.
They also said the treaty underpinning deportations must be "fully implemented" before flights take off.
The bill will continue its passage through the Lords on Wednesday when opposition peers could inflict further defeats.
However, the government is likely to overturn these when it returns to the Commons - likely later this month.
The bill is a key part of the government's plan to "stop" small boats crossing the English Channel, which Rishi Sunak has made a priority for his premiership. Ministers want flights to Rwanda to begin this spring.
Ministers unveiled the draft law late last year after its scheme to send an unspecified number of asylum seekers to the East African country was ruled unlawful by the Supreme Court.
In a attempt to resurrect the scheme and prevent legal challenges blocking future deportations, it would say Rwanda is a safe country in UK law and restrict the ability of the courts to block them on human rights grounds.
The government argues this is a necessary step to ensure deportations are not derailed by legal challenges.
But critics, including some Conservatives, say it will put people at risk and also undermine the independence of the courts.
In a series of votes earlier, opposition peers backed an amendment that would enable courts to overrule the presumption Rwanda is safe, if they see "credible evidence to the contrary".
The amendment, proposed by crossbench peer Lord Anderson of Ipswich, was also supported by a handful of Conservatives, including former home secretary Lord Clarke of Nottingham.
Lord Anderson added: "If Rwanda is safe as the government would have us declare, it has nothing to fear from such scrutiny".
Peers also approved changes that would mean Rwanda could only be deemed safe when independent officials overseeing the UK's deportation treaty with the country say it has been "fully implemented".
They also backed a Labour amendment that specifies the bill must maintain "full compliance with domestic and international law".
'Merry-go-round' of challenges
The government says its new treaty with Rwanda, signed in December, addresses the Supreme Court's objections.
Home Office Minister Lord Sharpe of Epsom said the treaty, which replaced an earlier deal, would mean there was no risk of people sent to Rwanda being sent on to their home countries, where they could face persecution.
Outlining why he rejected the amendments, he said the legal grounds for challenging deportations should remain "limited," in order to "prevent the merry-go-round of legal challenges".
"We cannot allow systematic legal challenges to continue to frustrate and delay removals," he added.
The changes made to the bill will now go back to the Commons, where the government has a majority and is likely to overturn them.
If the changes are rejected the bill will then undergo a process known as "ping pong", expected later this month, where it would go between MPs and peers until they can agree on the final wording.
Labour has suggested its peers will not seek to block the bill's passage into law completely, although Lord Coaker, one of the party's whips, said ministers should "listen" to objections raised in the Lords.