By Philip Blenkinsop and Robert-Jan Bartunek

BRUSSELS (Reuters) - Belgium declared on Monday that it could not formally back a free trade deal between the European Union and Canada because of an internal dispute, but the two sides still appeared to be holding out hopes of a summit to sign off on the deal.

Belgium's French-speaking Wallonia region opposes the Comprehensive Economic and Trade Agreement (CETA), which needs the unanimous support of all 28 EU nations to be approved.

The EU had given Belgium until late on Monday to overcome that opposition or the EU-Canada summit on Thursday to sign the pact with Canadian Prime Minister Justin Trudeau would be cancelled.

Belgian Prime Minister Charles Michel said he could not give consent. But European Council President Donald Tusk said he and Trudeau still believed the summit could go ahead.

"Together with PM @JustinTrudeau, we think Thursday's summit still possible," Tusk said in a tweet. "We encourage all parties to find a solution. There's yet time."

In Ottawa, a Trudeau spokesman said the Canadian prime minister and Tusk agreed to stay in close contact "in the coming hours and days".

Canadian Trade Minister Chrystia Freeland said "CETA isn't dead" but she sidestepped questions about what would happen if the EU failed to come to an agreement this week.

"We wish them well and we hope they can get there ... this deal is done - it's time to move on, get it signed and then get it ratified," she told reporters in the Canadian capital.

Michel, whose federal government backs the agreement, had called a meeting of the heads of Belgium's regions and linguistic communities.

"We cannot give a 'Yes'," Wallonia premier Paul Magnette told reporters afterwards. He said the main problems remained not with Ottawa, which has already agreed to modifications in the deal, but with the EU authorities.

Other Socialist Party-led authorities, including those of the bilingual capital Brussels, have thrown their weight behind the Walloons, while Dutch- and German-speakers back Michel's centre-right coalition.

The issue goes beyond just a trade deal with Canada, the EU's 12th-largest trading partner.

If CETA fails, the EU's hopes of completing similar deals with the United States or Japan would be in tatters, undermining a bloc already battered by Britain's vote to leave it and disputes over Europe's migration crisis.

"These are dark days for European trade policy," said Ulrich Grillo, president of the Federation of German Industries. "This blockade is undermining the trust of international partners in the EU."

PRINCIPLES OR INTERNAL POLITICS?

Geert Bourgeois, premier of the Dutch-speaking Flanders region, called the situation a real shame.

"We're the laughing stock of the whole world. It's bad for Wallonia, for Flanders, for Belgium, for Europe, for the whole world," he told reporters after the meeting.

EU negotiators say they are willing to keep talking with the Walloons. Freeland left in frustration after talks in the regional capital, Namur, on Friday, saying the problems were internal ones for the Europeans to sort out.

Andre Antoine, the Walloon parliament speaker, told Reuters earlier on Monday that more time was needed: "A reasonable time frame would be the end of the year. With that, we could get there."

CETA supporters say the deal would increase trade between the partners by 20 percent and boost the EU economy by 12 billion euros ($13 billion) a year and Canada's by C$12 billion ($9 billion).

Magnette's main objection is to an investor protection system that would allow foreign companies to sue host states they deem are harming their investments. Critics argue it enables multinationals to dictate public policy.

The European Commission says CETA has overhauled this system, with guarantees on the right of governments to regulate and judges appointed by EU and Canada rather than parties to a dispute.

Many EU leaders suspect the local government in Namur is using its devolved powers to play domestic politics.

(Additional reporting by Noah Barkin in Berlin and David Ljunggren in Ottawa; Writing by Philip Blenkinsop and Alastair Macdonald; Editing by Richard Balmforth and Paul Simao)