Speaking in Strasbourg on Tuesday, ALDE group leader Guy Verhofstadt said, "The EU is not in a good state and many are falling into the trap of nationalism and populism.
"It's one reason why we need to regain the trust and confidence of citizens."
This was echoed by EPP group Chair Manfred Weber, who said, "Europe is splitting and is fractured. We have to mend it and bring it back together again."
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Their comments come ahead of a set piece 'state of the union' speech by Commission President Jean-Claude Juncker on Wednesday and Friday's informal summit in Bratislava, which will take place without the UK.
Looking ahead to the summit, Weber told reporters, "The summit will go ahead without the UK so perhaps Europe can make progress on Friday on matters such as defence policy and TTIP."
Greens/EFA group co-Chair Rebecca Harms agreed, but suggested the EU should do more to promote itself and respond more effectively to emergencies such as the current refugee crisis.
The German MEP said, "I still believe the EU is, to a large extent, a success. But the EU has got to be much clearer in spelling out its successes and achievements."
One example of this, according to her co leader Philippe Lamberts, is its efforts on tackling tax avoidance as was evidenced, he said, in the recent EU ruling against Apple.
Meanwhile, Verhofstadt has called on EU leaders to "commit" to a proposed EU defence union when they converge on Bratislava at the end of the week.
He said, "With Brexit, Russian expansion and current events in the US, we in Europe can no longer rely on others to provide security in our neighbourhood.
"Look at what's happening in Syria and Ukraine - we can no longer say security is the business for the U.S."
He pointed out that the idea for a defence union was "not new", but had been given new impetus by the UK's EU referendum.