By Alastair Macdonald

BRATISLAVA (Reuters) - European Council president Donald Tusk called on EU leaders to take a "brutally honest" look at the bloc's problems as they met in Bratislava to find a way forward after Britain's shock vote to leave.

"We must not let this crisis go to waste," Tusk told reporters on his arrival in the Slovak capital on Thursday.

With British Prime Minister Theresa May absent, the other 27 leaders will gather on Friday to try and agree a diagnosis of why people across the bloc are increasingly voting for eurosceptic parties and on ways to regain trust in the EU.

"We haven't come to Bratislava to comfort each other or even worse to deny the real challenges we face in this particular moment in the history of our community after the vote in the UK," said Tusk, who will chair the summit.

"We can't start our discussion ... with this kind of blissful conviction that nothing is wrong, that everything was and is OK,” he added. “We have to assure ... our citizens that we have learned the lesson from Brexit and we are able to bring back stability and a sense of security and effective protection."

With governments deeply divided, between east and west, north and south, over how to bolster the economy and the euro zone and respond to an influx of refugees, Tusk has highlighted three priorities for agreement -- on strengthening external border controls, combating terrorism and reassuring people of protection from adverse effects of economic globalization.

Leaders want the summit to begin a process of negotiations in the hope of agreeing further strategies when they meet in March in the Italian capital to mark the 60th anniversary of the Union's founding Treaty of Rome.

However, with leading powers France and Germany holding national elections over the coming year, the bloc's immediate scope for agreeing substantive new policies, notably on reforming the euro currency area and asylum rules, is limited.