The impasse over the EU/Canada trade deal illustrates the EU's "incapacity" to make decisions, says Parliament's S&D group leader Gianni Pittella.
Speaking in Strasbourg on Tuesday, the Italian deputy said the delay in signing the CETA agreement highlights "massive issues" for the EU.
"This raises a bigger issue of the EU's current incapacity to do politics. It is not just CETA, but a host of other things, including the migration crisis, where the EU seems unable to do anything because of vetos at so many different levels," he told a news conference.
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"The current situation with CETA shows the need for a major review of the decision making process in the EU."
Nevertheless, Pittella said he was still "confident" the deal would be signed, adding, "It has taken years to get this far so a short delay shouldn't be such a problem."
His comments about the EU's shortcomings were endorsed by Philippe Lamberts, Co-Chair of Parliament's Greens/EFA group.
Lamberts said that he had been surprised that objections by Wallonia had so far delayed the signing of CETA.
But the Flemish politician defended the right of the Belgian region to raise issues about the deal and accused the EU of treating national and regional parliaments with "intimidation and disdain" in its trade agreements.
He said, "This approach is fuel for the extreme right and if it carries on like this then people like Marine Le Pen may as well go on holiday, because the public are going to rebel."
Further reaction to the impasse that threatens to derail the whole agreement came from ALDE group leader Guy Verhofstadt.
The CETA pact was due to be signed at a summit in Brussels on Thursday with European Council President Donald Tusk and Canadian Prime Minister Justin Trudeau.
Verhofstadt said, "What the EU should do is say that it is treating this as a sole EU competence, in other words, a matter just for the EU. That, in my opinion, would be the best solution."
He said it was "unrealistic" to require national and regional parliaments to be given the power to authorise such deals, adding, "Let's remember there are another 30 similar agreements waiting to be signed off."
Elsewhere, former European trade Commissioner Peter Mandelson commented, "EU trade policy won't survive in a world where trade agreements have to be 'democratised' by every single national parliament and sub-legislature across the EU before they see the light of day."
Belgian Prime Minister Charles Michel said on Monday that he could not sign the deal because the Walloon Parliament had voted against the agreement.
According to press reports, Tusk and Trudeau resolved in an emergency phone call on Monday to continue efforts to try to save the deal.