Earlier, Donald Tusk, the European Council President, called on EU leaders to assure citizens they had learned lessons from Brexit and were able to "bring back stability and a sense of security".
He urged them to take a "sober and brutally honest" look at the bloc's problems.
The EU response to the influx of migrants is one of the most contentious points among members.
The summit host, Slovak Prime Minister Robert Fico, is one of a group of central and eastern European leaders who object to the EU quota system which distributes 160,000 refugees across the EU. The scheme, for refugees from Iraq, Syria and Eritrea, is aimed at easing the burden on Italy and Greece.
Mr Fico has said Slovakia will not accept "one single Muslim migrant" and has mounted a legal challenge to the scheme.
On Tuesday, Luxembourg's Foreign Minister Jean Asselborn called for Hungary to be suspended or even expelled from the EU because of its "massive violation" of fundamental values, specifically the government's treatment of refugees.
For France, the priority is border security in the wake of a number of Islamic extremist attacks in the country.
France and Germany have outlined plans to deepen European military co-operation, which were reinforced in the State of the Union address by European Commission President Jean-Claude Juncker on Wednesday, in which he called for a European military headquarters.
The UK's departure from the EU removes one of the biggest obstacles to stronger EU defence in tandem with Nato.
The one-day Bratislava meeting is set to be the first in a number of confidence-building meetings where a "roadmap" should be set up to culminate in a summit in March in the Italian capital Rome, when the 60th anniversary of the EU's founding Treaty of Rome will be celebrated.