The other 27 EU leaders are expected to use the two-day summit to endorse a deal struck last week on the key Brexit
separation issues after months of torturous negotiations.
Several leaders sought to play down the impact of the vote in the House of Commons, although Luxembourg Prime Minister Xavier Bettel warned: "It's not making her life easier."
May has struggled to assert her authority since losing her parliamentary majority in a June vote, and the latest setback will renew fears about her mandate for negotiations on the second phase.
Pro-European MPs declared they had taken back control of Brexit after amending a landmark piece of legislation to ensure that they must approve the final divorce deal.
Dutch Prime Minister Mark Rutte said May still had a "formidable stature", saying the agreement on the divorce deal "showed you should not underestimate her".
However, with British ministers only due to discuss the post-Brexit future next week, he warned that "we need from her to understand how she sees the future relationship".
After a deal covering Britain's financial settlement, the Irish border and expatriate rights, the next stage on talks will cover future trade relations and a post-Brexit transition.
EU President Donald Tusk acknowledged the negotiations would also be a test for the bloc's own unity, as it tries to push through a host of reforms after Britain's departure.
"I have no doubt that the real test of our unity will be the second phase of the Brexit talks," Tusk told reporters as he arrived at the summit.
He said a "lack of unity is very visible" on two key subjects facing the EU after Britain leaves: plans for a way forward on the migration crisis, and proposals for reforms of the eurozone.
European Commission chief Jean-Claude Juncker struck a deal with May on Brexit separation issues on December 8, saying Britain had made "sufficient progress" to move the talks onto trade.
May will tell leaders over dinner on Thursday that the agreement "required give and take by both sides, but a fair outcome has been achieved", a senior British government official said.
She told reporters on arriving: "I'm looking forward to discussing that deep and special partnership for the future."
But Tusk warned earlier this week of a "furious race against time" to reach a deal before Britain leaves the bloc on March 29, 2019.
The EU guidelines that leaders will approve on Friday say they will start talks on the transition in January but will not begin discussions on trade until March as it needs more clarity on Britain's goals, while security and defence will be covered later next year.
Questions also linger over the deal struck last week, after British Brexit minister David Davis appeared to suggest it was not legally enforceable.
There are particular concerns about London's guarantee there will be no frontier checks between Ireland and the British province of Northern Ireland, after the UK leaves the EU's single market and customs union.
Davis's comments prompted a warning by the EU that Britain must not backtrack, and Rutte repeated Thursday: "We cannot have a misunderstanding of what was agreed."
German Chancellor Angela Merkel added that while progress has been made, there were still "outstanding questions".
Elsewhere, the thorny subject of migration is set to dominate the summit, amid a row over Tusk's comments that quotas for sharing out refugees around the bloc to ease the burden on frontline states were "ineffective" and "highly divisive".
Greek Prime Minister Alexis Tsipras, whose country was worst-hit by the crisis, said the remarks were "aimless, ill- timed and pointless".
Germany, Sweden and Italy are also big supporters of the mandatory quotas. Eastern European states like Poland, Hungary, the Czech Republic and Slovakia, whose leaders met separately ahead of the summit, are strongly opposed.
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