Seven proposed changes, including a provision to ensure "due regard" for domestic and international law, were passed by peers.

The bill will now return to the Commons, but not until after Easter.

The legislation aims to revive the government's plan to send some asylum seekers to Rwanda.

It declares the east African country is safe, after deportation flights were stalled by the Supreme Court ruling the government's plan could lead to human rights breaches.

The scheme is central to the prime minister's pledge to "stop the boats" as it seeks to deter people from making the dangerous journey across the Channel.

Labour's proposals on domestic and international law were passed by 271 to 228 votes.

Opposing the amendment, Home Office Minister Lord Sharpe insisted there was nothing in the bill which conflicts with the UK's international obligations.

Meanwhile, peers also supported a proposal put forward by crossbench peer Lord Hope that Rwanda only be deemed a safe country once a treaty bringing in new safeguards has been fully implemented.

The amendment passed by 285 to 230 votes.

Another change to exempt individuals who have supported the UK armed forces overseas from deportation to Rwanda, which was proposed by Labour peer Lord Browne, was passed by 248 to 209 votes.

The bill must now return to the Commons in a process known as "ping pong", where it is batted between the two Parliamentary chambers until they can agree the final wording.

This is now expected to happen after MPs return from their Easter break on 15 April, according to a senior government source.

Labour's Home Affairs spokesman Lord Coaker said the party had no intention of blocking the bill completely.

However, a delay could threaten Downing Street's ambition to get the first flights off the ground this spring.

No 10 officials insist that even if the legislation is not passed until after Easter, their target date can still be met.

On Monday, MPs voted down 10 amendments to the draft law proposed by peers earlier this month and they are likely to again reject any further changes put forward in the House of Lords.

Home Office Minister Michael Tomlinson has described the proposals put forward by peers as "wrecking amendments".

Ahead of the Lords debate, Home Secretary James Cleverly urged peers to allow the bill to pass.

"The more this bill progresses, the more worried Labour get that, as we've always said, it will work and the more we've anticipated deliberate efforts from Labour to delay, disrupt or sabotage the scheme," he told the Daily Express.

"We remain focused on not letting that happen, and hope their lordships recognise it's time to let this bill pass so we can continue to stop the boats, and save lives."

Labour's Yvette Cooper, the shadow home secretary, said the Rwanda scheme was "a failing farce".

"If the Conservatives were ready to implement this, they would be bringing the bill back to complete the remaining stages next week and get on with it," she said.

"But because their plans aren't ready, they've decided to delay the bill as well, so they can try to blame everyone else for the chaos they have created, and the fact that they haven't got a proper plan."

Labour has said it would scrap the Rwanda scheme if it wins power, even if flights take off before the next general election.

However, asked if any individuals already sent to the country would be returned to the UK under a Labour government, a party spokesman said they would not, adding: "If the scheme is up and running you have to accept the decisions the government has already made."