It is the latest in a series of crisis meetings since Britain voted to leave the EU last June, but fears about the new US president have strengthened the sense that the bloc is now at a decisive moment in its history.
The first part of the meeting, which all 28 leaders will attend, will focus on the migration crisis amid warnings of a new surge in people making the dangerous sea crossing from Libya.
British premier Theresa May will miss the second part when the other 27 discuss the way ahead after Brexit, including a flagship summit in Rome in March to mark the EU's 60th anniversary.
With doubts growing over the Trump administration's commitment to the transatlantic alliance with Europe, the leaders will also discuss "international issues" facing the union.
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Tusk, who will chair the summit, warned this week that Trump was a "threat" to the EU along with Russian aggression, an increasingly assertive China and domestic populism.
But Tusk also echoed what many EU leaders have said - that Trump is a chance for a Europe to finally unify after Brexit and the eurozone crisis, and perhaps even take Washington's place in global politics and trade.
Unity has, however, often eluded the EU on the migration crisis, which has seen more than one million people flee war, poverty and oppression in Syria, the Middle East and North Africa.
The route from Libya to Italy has become the most pressing problem, after the EU cut sea crossings from Turkey to Greece by 98 per cent thanks to a deal with Ankara.
The leaders will agree steps to stop migrants taking boats in the first place, including help for the Libyan coastguard and border forces, according to a copy of a summit declaration seen by AFP.
With rights groups warning about terrible conditions caused by people smugglers, other steps include helping Libyan communities to host migrants and working with the UN refugee agency and the International Organisation for Migration, it says.