In a report the peers argued the Government should give a "unilateral" pledge to guarantee their rights as it was the "morally right thing to do".
It comes after another report from a think tank also called on the Prime Minister to make the move, suggesting it was "morally" wrong not to.
So far Ms May has said that she expects to take the step, but only as a part of a deal that would see the rights of British citizens confirmed in other EU states.
Baroness Kennedy of The Shaws, chairman of the House of Lords EU Justice Sub-Committee, said: "The Government is under a moral obligation to give a unilateral declaration immediately to safeguard the EU citizenship rights of all EU nationals in the UK when the UK withdraws from the EU.
"I also believe that such a gesture will stimulate reciprocal commitments from the other EU countries where UK citizens are currently living."
Baroness Kennedy said that for the last six months the lives of EU citizens in the UK and UK citizens in Europe had been "shrouded in anxiety" and they had no idea how to plan their futures.
She added: "Most shockingly the rise in xenophobic behaviour since the referendum has now meant that EU citizens who have contributed to the UK economy for years no longer feel welcome in the country they call home. We find that unacceptable."
Their report set out how the rights of an EU citizen to live and work in any member state, and to gain a permanent right of residence in that country after five years, are some of the most fundamental in EU law.
In the absence of a negotiated settlement the consequences of the loss of EU citizenship rights will be severe, according to their paper.
It highlighted "deep anxiety" among EU nationals, including Polish, Romanian and French people, in the UK as well as UK nationals living and working on the continent.
Even if the Government refuses to give a unilateral undertaking ahead of the negotiations, there is a strong case for agreeing EU citizenship rights as a preliminary and separate element of the negotiations as soon as Article 50 is triggered, the report said.
Earlier this week think tank British Future called for the Prime Minister to demonstrate "goodwill" and "make the first move" in giving EU citizens in the UK before Brexit the right to stay here permanently.
Meanwhile, the European Parliament’s chief negotiator Guy Verhofstadt has backed a plan to offer British citizens "associate citizenship" after Brexit.
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies