Spain has declared frustration with the agreement, largely based on the much-contested subject of Gibraltar.
The tiny territory at the tip of the Iberian Peninsula is under British rule, but Spain asserts a claim.
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In terms of the Brexit agreement, Spain wants the future of Gibraltar to be a bilateral issue between Madrid and London.
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There are concerns among Spanish officials that a clause within the agreement speaks of UK-EU relations with no mention of Gibraltar.
Spanish Prime Minister Pedro Sanchez has made his opinion clear, saying on Thursday Spain would be against the draft deal on Britain’s exit from the European Union if there are no changes.
He threatened that with no changes, Spain would vote against the deal on Sunday.
He said: “After my conversation with Theresa May, our positions remain far away. My government will always defend the interests of Spain.
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“If there are no changes, we will veto Brexit.”
A member of the European Union, the fate of Gibraltar post-Brexit and the more than 30,000 residents and 10,000 cross-border Spanish workers has been closely watched throughout negotiations.
Gibraltar’s Chief Minister Fabian Picardo said on Friday: ”We’ve worked very hard and have in fact reached agreement with Spanish colleagues in respect of Gibraltar’s role in the withdrawal process.
“If (the withdrawal agreement is) opened for one comma or one full-stop on Gibraltar, it’s going to be re-opened on any of the other issues.”
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EU diplomats hope the text could be agreed by late Friday but fear Mr Sanchez will want to discuss it at the top level on Sunday.
Fears are the Spanish Prime Minister will want to show determination and score points with voters at home ahead of Spain’s December regional election.
Chancellor Angela Merkel’s spokesman said Germany believed any outstanding questions would be cleared up in time for Sunday’s summit to go ahead.
“We assume that open questions can be cleared up by Sunday,” spokesman Steffen Seibert said.
“That is being worked on intensively, so the chancellor is preparing for the trip to Brussels.”
Determined to prevent redrafting of both the withdrawal treaty and the declaration on a new EU-UK relationship, and risk halting the extensive process, the EU states have suggested addressing Spain’s concerns in a separate statement given by the 27 leaders on Sunday.