The EU has rejected calls for an agreement to protect UK and EU expats' rights, if there is a no-deal Brexit.
Tory MP Alberto Costa quit his government job to table an amendment calling for the protections.
It was backed by the government in votes on Wednesday, with Mr Costa urging the PM to write to EU chiefs to demand an agreement on rights.
But the European Commission said it would "not negotiate mini deals" as it would imply negotiations had failed.
Theresa May's withdrawal deal includes pledges to protect the rights of UK citizens in EU states and EU citizens in the UK after Brexit.
But MPs have so far rejected Mrs May's deal - raising the prospect of the UK leaving the EU without a deal on 29 March.
Mr Costa's amendment called for the PM to write to the President of the European Council, Donald Tusk, to seek to guarantee the rights of EU nationals even under a no-deal Brexit.
He had to resign from his unpaid government role as a parliamentary private secretary to Scotland Secretary David Mundell, due to the convention that MPs serving in government should not amend government motions.
The amendment gained support from 141 MPs from different parties, and was accepted by the government. The amendment was approved unanimously by MPs, without a vote.
Speaking in the Commons , Mr Costa said he had "been a loyal Conservative member. I have never rebelled and have scarcely spoken out of turn".
But, he told MPs that EU citizens' rights "should have been dealt with at the outset of the United Kingdom's decision to leave the EU".
And he has accused the UK government of using citizens' rights as a "bargaining chip" in talks with Brussels.
Responding to Mr Costa's amendment, European Commission spokesperson, Mina Andreeva, said "the best way to protect the rights of these 4.5 million people concerned is through the withdrawal agreement.
"We will not negotiate mini deals, because negotiating such mini deals outside the withdrawal agreement would imply that the negotiations have failed.
"The Commission has consistently made clear that rights of EU citizens in the United Kingdom and UK nationals in the EU are our top priority, they should not pay the price for Brexit."
The Commission has urged EU member states to take a "generous approach" to UK citizens living abroad, she added.
Theresa May has said EU citizens in the UK will be able to stay even if there is no deal done on Brexit.
EU nationals with a right to permanent residence, which is granted after they have lived in the UK for five years, should not see their rights affected after Brexit.
But there is uncertainty about what no deal would mean for Britons living in France, Spain, Germany and elsewhere.
The priority for most will be to register as residents, but the rules - including deadlines for paperwork - vary from country to country.
Mrs May has promised MPs a meaningful vote on her deal by 12 March - just 17 days before the UK is set to leave the EU.
She has also committed to giving MPs a vote on delaying Brexit, if they reject both her deal and no-deal.