“We will be looking at the concrete progress that’s been made in our exit negotiations and setting out ambitious plans for the weeks ahead,” she said as she arrived for the two-day EU summit.
“I particularly want to see an urgency in reaching an agreement on citizens’ rights.”
The 27 other EU leaders are due to decide whether there has been “sufficient progress” in the first stage of Brexit talks, and if they can move on to discussing Britain’s future trading relationship.
But after five rounds of negotiations there remains a deadlock, notably on the question of Britain’s financial commitments, and the decision is expected to be delayed until the next EU summit in December.
May is due to plead her case with her fellow leaders at a working dinner on Thursday evening, before leaving them to make their decision without her on Friday morning.
The prime minister made a speech on Brexit in Florence last month, offering some concessions on the money and the rights of around three million European citizens living in Britain.
In a letter directly addressing European citizens on Thursday, May said Britain was within “touching distance” of a deal on guaranteeing their future, and vowed again that anyone living lawfully in Britain would not be asked to leave after Brexit.
But questions remain about their status if there is no deal before Britain automatically leaves the EU in March 2019.