Brexit Secretary David Davis wants to "accelerate" talks over the future rights of EU citizens living in the UK and EU-based Britons.
Fears have been raised over the post-Brexit rights of an estimated three million EU nationals based in the UK, with MPs urging the Government to guarantee they have a right to remain.
Ministers are seeking to ensure the rights of the 1.2 million Britons living in EU member states are protected before making any firm commitments.
Speaking in the Commons, Labour MP Gisela Stuart - who chaired the successful Vote Leave campaign - warned Davis that this issue must be treated as a "top priority".
She said: "Whether we were on the side of Remain or Leave, I think we should be on the side of doing things in the interests of the British public.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"In that context, you did mention the rights of EU citizens and you referred (to how) you are sure we could arrive at a general settlement.
"Could I suggest to you that people do worry about their future, whatever the legal framework is, and that these negotiations both with other EU member states and the rights of UK citizens there and here is a top priority because these uncertainties deserve to be settled as soon as possible."
Davis replied: "I agree with you that it's a high priority and if I can accelerate it, I will."
