Canada and the European Union say they remain hopeful a landmark free trade deal can go ahead despite three Belgian regions led by Wallonia blocking it.
European Council president Donald Tusk said it was still possible CETA could be signed as planned and Canada's trade minister said the deal was ‘not dead’.
But Belgium has said it cannot back the deal because three French-speaking parts of the country oppose it.
CETA needs the support of all 28 EU nations before it can be approved.
It is the EU's most ambitious free trade deal to date, and has been in the pipeline for seven years. The other 27 EU governments want to sign the agreement.
However, hopes it could be signed on Thursday appeared to be dashed on Monday when Belgian Prime Minister Charles Michel said he did not have the unanimous approval of his country's federal, regional and community bodies.
He said talks with Wallonia, a staunchly socialist region of 3.6 million people, and two other elected bodies had failed.
Despite this, Tusk remained upbeat after speaking to Canadian PM Justin Trudeau about CETA - the Comprehensive Economic and Trade Agreement - on Monday.
In a tweet, Tusk wrote: ‘Together with PM @JustinTrudeau, we think Thursday's summit [is] still possible. We encourage all parties to find a solution. There's yet time.’
Chrystia Freeland, Canada's federal minister for international trade, said she too remained hopeful the deal can be salvaged, but that ‘the ball is in Europe's court’.
The European Commission, which has negotiated the deal on behalf of the 28 nations, had asked Belgium to make its decision by Monday.
But it later insisted that Thursday's summit was not the final deadline for the deal to be signed.
‘Now, we need patience,’ EU Commission spokesman Margaritis Schinas said. ‘The Commission traditionally does not set deadlines or ultimatums.’
Wallonia has led objections to the deal, demanding stronger safeguards on labour, environmental and consumer standards.
But at talks with Martin on Monday, it emerged two other administrative bodies also opposed CETA - Brussels and that of the country's French-speaking community.
The Belgian socialists' fears echo those of anti-globalisation activists, who say CETA and deals like it give too much power to multinationals, granting power even to intimidate governments.
There have also been big demonstrations in several EU countries against CETA and the TTIP trade talks between the EU and the US.
Canada and the EU would eliminate 98 per cent of tariffs under CETA, which was negotiated between 2009 and 2014.
Supporters say this would increase trade between them by 20 per cent, and would especially help small businesses.
Critics say the deal threatens product standards and protects big business, allowing corporations to sue governments.
On Monday, Wallonia's regional leader Paul Magnette warned: ‘We will never decide anything under an ultimatum or under pressure.’
His counterpart in Belgium's Dutch-speaking Flanders region, Geert Bourgeois, said the blockage was ‘a real shame’.
‘We're the laughing stock of the whole world,’ said the centre-right leader, quoted by Reuters news agency.
Some UK politicians see CETA as a potential model for a Brexit trade deal with the EU.
CETA does not involve EU-style free movement of labour. But for British services – 80 per cent of the UK economy - the CETA terms are less favourable than those they have now.
Want stories like this in your inbox?
Sign up to exclusive daily email
More Stories from Trade & Commerce