Arriving for a special summit in Brussels, European Commission President Jean-Claude Juncker, head of the bloc's executive arm, said it was a "sad day".
Earlier on Friday, Spanish officials in Brussels said Sanchez might not attend the summit if London fails to put into writing a promise that no future agreement between Britain and the European Union that applies to Gibraltar can be signed without first being negotiated on a bilateral basis with Spain.
Sanchez had said on Friday he wouldn't back the divorce deal United Kingdom and European Union leaders are supposed to vote on during Sunday's summit in Brussels, saying a draft agreement did not include clear language regarding Gibraltar. He said it would greatly reduce Britain's influence and ability to make independent trade deals.
The prime minister arrived in Brussels as European Union leaders prepare to approve the UK's withdrawal agreement, which had been threatened by a diplomatic row with Madrid.
The Democratic Unionist Party, whose votes from Northern Ireland have helped May to govern since she lost her majority in a snap election a year ago, said it would try to block a Brexit deal it called "pitiful" - partly because it binds London to many European Union rules it will no longer help set and partly as the DUP fears it could weaken the province's ties to Britain. "This is the deal that is on the table, this is the best possible deal, this is the only possible deal".
"It would not be a good idea to lecture the House", Juncker said, but insisted that it was only deal possible.
"I will always stand by Gibraltar", May said.
The deputy leader of the Democratic Unionist Party in Northern Ireland has used a party conference speech to try to persuade Prime Minister Theresa May to change course on Brexit.
Spain said Friday it wouldn't back the divorce deal United Kingdom and European Union leaders are supposed to vote on during Sunday's summit in Brussels after language regarding Gibraltar didn't appear in a draft agreement.
"We have worked through the withdrawal issues for Gibraltar in a constructive and sensible way", she said.
He said he had received the written guarantees he needed over Spain's role in the future of the British territory. Unlike the withdrawal agreement, which will be legally binding after it is approved by British and European parliaments, the political document is loosely worded and aspirational, an outline for future talks, which will likely take years to complete.
May declined to say when asked by a caller whether she would resign if the deal was rejected by Parliament.
Britain will leave the European Union on March 29 but remain inside the bloc's single market and be bound by its rules until the end of December 2020, while the two sides work out a new trade relationship.
"We have an agreement that allows for an orderly withdrawal".
This position was backed by Dutch Prime Minister Mark Rutte. That pledge, which the prime minister has previously claimed is the result of a "Brexit dividend", echoes the £350m a week the Vote Leave campaign claimed on its battlebuses could be diverted to the the health service if Britain left the EU.
It comes after Spanish Prime Minister Pedro Sanchez received assurances from the United Kingdom government over Gibraltar, and dropped his threat to boycott the summit, BBC reported on Saturday. "The British people don't want to spend any more time arguing about Brexit", she said.
Her limits as vote-wrangler will be tested in her own Parliament, where pro-Brexit lawmakers have hammered the plan as failing to break decisively enough from Brussels and pro-E.U. forces have condemned it as a self-inflicted wound that hurts British voters.
The compromise brokered during through-the-night talks saw the green light given to Sunday's emergency European Council, where the likes of German chancellor Angela Merkel will wave through the Brexit deal which has been negotiated over the last 18 months.