The barb from an emotional Chrystia Freeland, the Canadian trade minister, fed into warnings by EU leaders that the 28-nation bloc may now never be able to land any other deals including one with the United States.
"It seems obvious to me, to Canada, that the European Union is incapable now of having an international agreement, even with a country with such European values as Canada, and even with a country as kind and patient as Canada," Freeland said on Belgian television.
"I worked very, very hard, but I think it's impossible. We have decided to return home and I am very, very sad. It's really emotional for me. The only good thing for me is that tomorrow morning I will be with my three children," she added.
A source at the European Commission, the executive of the EU, confirmed the talks have "come to a halt" but told AFP the "Commission doesn't consider that this is the end of the process."
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There have been protests against both deals in several cities.
Freeland was speaking after marathon talks in the walled Wallonian capital of Namur with local leader Paul Magnette and an EU official.
The talks were closely watched in Brussels where EU leaders were pressuring Wallonia to stop blocking the trade deal, which requires the support of all 28 EU member states.
Canadian Prime Minister Justin Trudeau had planned to visit Brussels next week to sign the deal but that looks almost certain to be called off.
European Commission President Jean-Claude Juncker told a closing summit press conference earlier that he still hoped a deal would be finalised in a few days, but could not hide his frustration over the failure to conclude a pact he strongly backed.