EU leaders are due to ratify the draft divorce deal at a European Council meeting on Sunday but Spain said this week that it can not support the agreement unless it is given a clear veto on Gibraltar's inclusion within the negotiations on the future relationship.
But the declaration does not deal with the vexed issues of fishing and Gibraltar, the British territory that sits on an outcrop of southern Spain. Spain has long claimed sovereignty over the territory.
Spain maintains a claim to Gibraltar after it was ceded to the British crown under the 1713 Treaty Of Utrecht, and through the Brexit negotiations Spain has conducted separate talks with the United Kingdom government over the future of the border.
The government of Spain said on Tuesday that it would vote to reject the EU's draft Brexit agreement.
But Spain wants to retain what it sees as its right to negotiate the future on Gibraltar with Britain on a bilateral basis, giving it an effective veto.
The 585-page, legally binding withdrawal agreement is as good as complete, but Britain and the European Union still need to flesh out a far less-detailed declaration on their future relations. Previously, wants to meet Jun again with European Commission President Jean-Claude Juncker.
Earlier, new Work and Pensions Secretary, Amber Rudd, noted that parliament "will stop" a no-deal Brexit, appearing to contradict previous statements from the PM who had warned that failure to back her deal could lead to such a scenario.
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Downing Street has repeatedly made clear that agreement is needed on the future framework - setting out aspirations in areas like trade and security co-operation and believed to run to a few dozen pages - in order to press ahead with the legally-binding withdrawal agreement.
There was speculation that the Prime Minister was struggling to keep her Brexit deal alive, after she announced following her meeting with Mr Juncker that she would return to Brussels on Saturday for further talks.
"I will do everything possible to get an exit agreement", she said.
While Spain last week initially welcomed a protocol on Gibraltar in the draft Brexit agreement, Foreign Minister Josep Borrell on Monday said there was confusion over Gibraltar in the main body of the agreement.
The European Commission's chief spokesperson Margaritis Schinas said today that the EU is "working closely" with the member states to resolve the issue.
May won a reprieve from some of her Conservative Party foes after pro-Brexit rebels acknowledged that a bid to trigger a no-confidence vote in May had failed, for now.
She added: "We would already have an agreement if it weren't for the (Irish border)".