French President Emmanuel Macron, attending his first summit, warned countries against defying Europe's principles and values, as some eastern European states challenge the bloc's refugee-sharing scheme, which was adopted with a legally binding majority vote.
The agenda will be dominated by Brexit, but also cover the start of the process of moving two UK-based agencies - the European Medicines Agency (EMA) and European Banking Authority (EBA). It's not up to me to say it's closed.
However, after May is finished with her talk during Thursday's dinner, leaders are not expected to quiz the British PM.
But May's disastrous showing in elections on June 8 in which she lost her majority has sparked speculation that her Brexit plans may be watered down, or even reversed.
The cut-off date is yet to be set, but will come between the day when Britain formally notified Brussels of its intention to quit on April 29 2017 and the day when it finally leaves, expected to be March 29 2019.
But Tusk, who has repeatedly said Brexit benefits no one, especially not Britain, channeled former Beatles John Lennon as he became the latest in a series of European Union leaders to suggest it was not too late to change tack.
A British official said May would offer "new elements" in a paper on citizens' rights to be published next week.
There would be no changes until the latter date: "All EU citizens now (in Britain) will have their rights protected under EU law until the date we leave the EU", the source said.
Brexit talks kicked off on Monday, and the EU's chief negotiator, Michel Barnier, will brief European Union leaders after May has left the room on Thursday night.
"The election result was not the one I hoped for, but this government will respond with humility and resolve to the message the electorate sent", May said in remarks introducing the policy plan.
But her wings have been clipped - not only in Britain where voters denied her a majority in parliament, but also in Brussels where European Union leaders will try to stop her from discussing Brexit beyond a quick presentation.
Tusk told the leaders in an invitation letter that after a series of election defeats for anti-migrant parties, notably in France, the European Union is "slowly turning the corner".
French president Emmanuel Macron and German chancellor Angela Merkel are expected to recommend another six-month rollover of tough economic sanctions imposed in 2014 against Russian Federation over the conflict in eastern Ukraine.
"So who knows? You may say I am a dreamer but I'm not the only one", Tusk continued, quoting a lyric from the late John Lennon's "Imagine". What impact has the decision had on your life?
In a two-day summit whose agenda is formally dominated by immigration, security and the economy, Mrs May will also brief her counterparts on the UK's commitment to a new £75 million plan created to stem the flow of illegal migrants from Africa to Europe.