Spanish Prime Minister Pedro Sanchez said on Wednesday that they would reject the draft Brexit withdrawal deal if there is no clarification on the future of Gibraltar - a British overseas territory.
"As it stands, the [Spanish] government will vote against the Brexit agreement", he said.
Borrell warned that his country's support for the deal is now contingent on the content of the political declaration on the future ties between the two sides.
Spain has been seeking assurances this week over the status of Gibraltar, the small peninsula on its southern coast that has been a British territory since 1713.
Under the proposed deal, the EU accepted the idea of a whole-U.K. customs union with the bloc, in a major concession to please United Kingdom demands to protect its territorial integrity.
Spain is threatening to reject the draft Brexit deal over the territory of Gibraltar while European Union leaders meet in Brussels to sign off on the future relationship between the European Union and UK.
The PM said she was pleased that the UK had agreed a protocol on Gibraltar that would form part of a wider package of agreements between the UK, Spain and the Government of Gibraltar setting out the parties commitment to co-operation.
Her remarks appeared mainly aimed at Spain, which has raised concerns about the treatment of Gibraltar in the proposed text, and France, which is leading calls for improved access to British fishing waters.
Brexit needs an explicit carve-out for Gibraltar, Spain's foreign minister and prime minister said Tuesday.
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But May reassured British lawmakers that "we will not exclude Gibraltar from our negotiations on the future relationship".
The Withdrawal Agreement is a legally-binding treaty that has been tough to negotiate and neither London or Brussels are willing to reopen it to address the Spanish objections.
After the Brexit referendum, in which Gibraltarians voted massively to stay in Europe while mainland Britain voted out, London and Madrid began bilateral talks on matters of disagreement - but not of sovereignty.
These agreements will be negotiated between Brexit day on March 29, 2019 and December 2020 - extendable once - and will enter into force at the end of the period.
"The right thing to do is to accept the deal and to get the future relationship and make sure we never go into the backstop in any way".
"It is not exorbitant at all, we have special legitimacy to ask for it", a Madrid government source told AFP.
The controversial withdrawal agreement is the result of months of negotiations on both sides and is aimed at preventing the prospect of Britain crashing out of the European Union without any deal.
But while the 585-page, legally binding withdrawal agreement is complete, Britain and the European Union still need to flesh out their far less detailed seven-page declaration on future relations.
"Yesterday I was with United Kingdom negotiators, who were accompanied by top Gibraltarian officials, and I can assure you that this was repeatedly made clear, as it has been in all our meetings".