Meanwhile, European Council President Donald Tusk said the bloc was determined to have as close as possible a partnership with Britain, which has always been sceptical about deeper EU integration.
The European Union removed the last major obstacle to sealing an agreement on Brexit after Spain said it had reached a deal Saturday with Britain over Gibraltar on the eve of a summit where EU leaders will sign off on the divorce papers.
Spanish Prime Minister Pedro Sanchez previously expressed concerns about the future of Gibraltar, the British territory of less than 3 square miles on Spain's southern coast.
A possible rejection of Sunday's Brexit deal in the British parliament will not prod the European Union to turn to any Plan B on the UK's withdrawal from the bloc, Reuters cited an unnamed senior EU official as saying.
The outlines of that campaign were clear as she described the merits of the deal on Sunday, highlighting an end to free movement "once and for all"; halting "vast annual payments" to the EU, and ending the jurisdiction of the European court of justice as the advantages of her deal.
May was quick to correct her Spanish counterpart, saying: "The UK's position on the sovereignty of Gibraltar has not changed and will not change".
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A vote on the motion to speed the legislation through the Commons could come as early as Friday. Meanwhile, the federal government is trying to push a back-to-work bill through the Commons.
"I don't think (the EU) are going to come to us and say, 'We'll give you a better deal, '" she added.
"I'll take this deal back to the House of Commons confident we've achieved the best deal available and full of optimism about the future of our country", May said at a news conference in Brussels.
But it is another concession that British Prime Minister Theresa May has made in order to secure a deal ahead of Britain's departure from the E.U.in March.
May herself repeated this, telling reporters in Brussels: "This is the best possible deal, it's the only possible deal".
Labour Party leader Jeremy Corbyn said on Sunday his party will oppose May's Brexit deal in the parliament, describing it as a "miserable failure of negotiation that leaves us with the worst of all worlds".
Spain wants to discuss the future of the British Overseas Territory - over which it holds a historic claim - on a bilateral basis and completely separate from the future EU-UK talks.
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"It is a deal for a brighter future, which enables us to seize the opportunities that lie ahead", she said.
But he said terms had been agreed that would "reduce the risks and losses", and recommended that European Union leaders sign off on the deal. That means to organize in an orderly fashion the withdrawal decided by the United Kingdom.
Spain was furious that the article did not explicitly state that the deal would not apply to Gibraltar without their agreement - a condition that appeared in the negotiating guidelines given by the European Council to the EU chief Brexit negotiator Michel Barnier at the outset of the Brexit process.
Mr Tusk said the Brexit deal reached by negotiators from the United Kingdom and Brussels "found the best possible compromise" and he would recommend that they approve it.
European Parliament president Antonio Tajani said a "large majority" of MEPs were in favour of the deal.
A vote is expected in December. Nothing better sums up the 26-page declaration on post-Brexit relations: it promises everything and nothing.
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Obviously, the mall was packed with people doing their early Black Friday shopping , and chaos erupted when the shots were fired. There is no other information at this time. "Oh, they shooting in this house", a woman screams as the shots ring out.
May insists her deal delivers on the things that matter most to pro-Brexit voters - control of budgets, immigration policy and laws - while retaining close ties to the UK's European neighbours.