Home Secretary Amber Rudd has written to every peer urging them to leave the Government's Brexit Bill alone as ministers face the prospect of a first defeat in the Lords for the legislation.
A Labour amendment to the EU (Notification Of Withdrawal) Bill guaranteeing the status of EU nationals living in the UK after Brexit could cause the Government problems on Wednesday.
Ministers have faced criticism - including from some Conservative MPs and peers - for treating EU citizens in the UK as "bargaining chips" in forthcoming negotiations on Britain's withdrawal.
In her letter, Ms Rudd insisted the Government was committed to treating EU nationals with the "utmost respect" but said ministers needed to be able to protect the rights of British nationals living in the EU in the negotiations.
"There is absolutely no question of treating EU citizens with anything other than the utmost respect.
"That's why we will be making securing their status a priority as soon as we trigger Article 50 and the negotiations begin.
"A unilateral move by the Government to address the issues facing EU nationals in the UK, however well-intentioned, will not help the situation of the hundreds of thousands of our own citizens in the EU.
"They could end up facing two years of uncertainty if any urgency to resolve their status were removed by the UK making a one-sided guarantee.
"We need to act fairly and provide certainty for both groups of people as quickly as possible, and that will remain the Government's position."
Labour's leader in the Lords, Baroness Smith of Basildon, said Ms Rudd's response was "deeply disappointing" and underlined the need for a vote to give the Government and MPs a chance to "to think this issue through and reconsider".
"To continue to use people as bargaining chips in this way is not only shameful but could have a dire impact on the UK's economy and essential services," she said.
"Confirming the rights of those EU citizens living in the UK can only be of benefit to our citizens worried about their future in EU countries but the Government's approach seems to be to sit back and wait for others to blink first."
Lord Newby, the leader of the Liberal Democrats in the Lords who are also backing the amendment, said: "This is a vital amendment that will put pressure on MPs to see sense and give reassurances to the millions of EU nationals living in the UK.
"Passing the amendment will require the Commons to think again.
"This is the role of the Lords and empty threats will not stop us voting to improve and rectify injustices in the Government's drive towards a hard Brexit."
The Government has no overall majority in the Lords. If the amendment is passed, ministers will still have the option of trying to overturn it in the Commons.
If they succeed it would then "ping pong" back to the Lords, where it is thought peers are unlikely to force a second vote.