Former Labour minister Lord Mandelson has urged peers not to “throw in the towel” when they debate legislation paving the way for Brexit.
He said the Lords should amend a bill to protect the rights of EU citizens to ensure a “meaningful” vote on the final deal before Britain leaves the EU.
He urged fellow Labour peers to show “strength and clarity” over the issue.
Conservative Justice Secretary Liz Truss said Brexit opponents were “fighting yesterday’s battles”.
The House of Lords – in which the government does not have an in-built majority – will start considering proposed legislation to leave the EU on Monday.
But the former Labour cabinet minister, EU Trade commissioner and Remain campaigner said the “verbal guarantees” the government were offering EU citizens in the UK were insufficient.
Lord Mandelson told the Andrew Marr programme that the Lords should “reinstate” the protections into the bill in the coming weeks.
“The government used its majority to bulldoze the legislation through the House of Commons,” he said. “I hope it won’t be so successful in the House of Lords,” he said.
“At the end of the day the House of Commons, as the elected chamber, will prevail but I hope the House of Lords will not throw in the towel early.”
But Ms Truss said leaving the EU was the “settled will” of the British people and the House of Lords needed to “get on” with the process.
She told Andrew Marr that once the UK formally notified the EU of its intention to leave by triggering Article 50, she believed the process was “irrevocable”.
Earlier this month, MPs overwhelmingly backed a bill to empower Theresa May to begin the Brexit process. The PM wants to do this by the end of March but needs the approval of both Houses of Parliament first.
MPs rejected calls for the status of EU citizens living in the UK and a parliamentary vote on the final terms of exit to be explicitly guaranteed in the bill – although ministers have conceded the Commons will have its say and it fully expects citizens of other EU countries to be able to stay in the UK after Brexit pending negotiations.
Lord Mandelson also said some Leave voters who were having second thoughts at the government’s “Brexit at all costs strategy” needed to have their voice heard.
But Ms Truss said Lord Mandelson was speaking as if the referendum “never happened”.
She told Andrew Marr that the House of Commons had “conclusively” voted to trigger Article 50, with the majority of Labour MPs backing the government.
“The fact is it is a simple bill on whether we trigger Article 50,” she said.
“The British people have voted for that and was clear in the referendum.
“The House of Lords now needs to get on with it. I fully expect the House of Lords will recognise the will of the people and the House of Commons.”
Although she voted to remain in the EU last year, Ms Truss said there was now a “new reality” and if a similar vote was held in the future, she would vote to leave.
Tory backbencher Dominic Raab warned the Lords would face a backlash if it tried to hold up the Brexit process.
“Voters will not look kindly on unelected politicians seeking to obstruct both the result of the referendum, and the vote of their elected representatives in the House of Commons earlier this month,” he said.