Brexit Secretary David Davis has called on both sides in the negotiations on the UK's departure from the European Union to "get down to business".
David Davis is in Brussels for a second round of formal talks on Brexit, BBC reports.
He said his priority was to "lift the uncertainty" for EU citizens living in the UK and Britons living in the EU.
The EU says there must be substantial progress on this - and on a financial settlement and the issue of the Irish border - before trade talks can begin. "We made a good start last month, and this week we'll be getting into the real substance."
"Protecting the rights of all our citizens is the priority for me going into this round and I'm clear that it's something we must make real progress on."
Earlier this month, Theresa May's offer to give the three million EU citizens in the UK "settled status" after Brexit was immediately dismissed by European Council President Donald Tusk as "below our expectations".
Michel Barnier, the European Commission's chief Brexit negotiator, has said there are still major differences between the EU and UK on the rights of EU citizens living in Britain.
Barnier has said that citizen rights - along with the "divorce payment" and border issues - must be dealt with before future UK-EU trade could be discussed.
The financial payment the EU says will be owed to cover the UK's commitments is also a key point for Barnier. Estimates have put the amount at anywhere from €60bn to €100bn (£53-89bn).
But in the Commons, Foreign Secretary Boris Johnson has said that Brussels could "go whistle" if it expected the UK to pay a hefty "divorce bill".
In response to Johnson's comment, Barnier said: "I'm not hearing any whistling. Just the clock ticking."
Talks are expected to continue to Thursday.
