The transition period, which would come into force when Britain officially leaves the EU in March 2019, is meant to be a temporary arrangement to continue the current UK-EU relationship while a future trade deal is negotiated.
Sanchez didn't go into detail about the agreement over the tiny territory on Spain's southern border, which London has controlled for three centuries against Madrid's wishes.
"There is a message of goodwill, readiness to reach an agreement".
When the leaders gathered in the Belgian capital on Wednesday, they were determined to avoid another diplomatic catastrophe like Salzburg.
Speaking at a press conference in Brussels, May said: "There is a lot of hard work ahead, there will be more difficult moments as we enter the final stages of the talks, but I'm convinced we will secure a good deal that is in the interests of the United Kingdom and of the European Union".
Yet if a deal is to be struck, the focus will be finding a formulation that makes a customs border between Northern Ireland and the British mainland highly improbable and/or makes a UK-EU future customs zone more certain than Brussels now wants.
"An extended transition period means the United Kingdom continues to "pay but have no say" in Brussels".
He also warned that a hard border between Ireland and Northern Ireland could lead to violence.
Tajani said May said she would evaluate an idea to extend the post-Brexit transition period by a year from the current cut-off date at the end of 2020 but that the British prime minister did not say whether she would favour that, or not. "That's a good idea", European Commission chief Jean-Claude Juncker said.
He added that "this is giving us some room to prepare the future relations in the best way possible".
Chancellor Angela Merkel's spokesman said that members also discussed cybersecurity, migration, and the continued development of the Eurozone. But she said she didn't believe the extension would be needed.
"My working assumption is not that we will have a no-deal, a no-deal would be risky for Britain and the European Union". "Where there's a will, there should be a way, and normally there is a way".
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An undated photo of missing 13-year-old Jayme Closs of Barron, Wisconsin. "I just want to bring Jayme home". The 13-year-old's whereabouts and safety are still in question as a search for her enters another day.
Her concession of a longer transition is part of a bid to break a deadlock over how to avoid border checks being reimposed along the 500-kilometer frontier separating the Republic of Ireland from Northern Ireland when Britain leaves the European Union.
It has been a tough week for Theresa May, who has spent the last few days in Brussels at a crunch Brexit summit with European Union leaders.
"This is not expected to be used", May said, "because we are working to ensure that we have the future relationship in place by the end of 2020".
There was a glimmer of progress around a proposal to extend a post-Brexit transition period to give more time for a new U.K. -EU trade deal - but that is fiercely opposed by May's pro-Brexit critics at home.
As the March 29 deadline for the UK's exit from the union looms, there's more uncertainty the ever.
EU Council President Donald Tusk says this week's summit with British Prime Minister Theresa May has left him more optimistic that a Brexit deal can be found for Britain's divorce from the bloc. This is just one of many huge risks May will have to take in the coming weeks.
Broadcasting from the EU Parliament in Brussels, Nigel was seething.
And we'll have no prospect of leaving because there will be no incentive to negotiate with us.
British Foreign Secretary Boris Johnson, ex-Brexit Secretary David Davis and other from May's party warned the prime minister not to "engage in a show of resistance and a choreographed argument followed by surrender" to the EU.
"If Theresa May is asking for a longer transition period, she is stalling", said Tory MP Nadine Dorries.
Mrs May, who had been called upon to table new proposals on the Irish Border backstop, was thought to have been "developing her thinking".
Tajani said he raised with May the possibility that the post-Brexit transition period, during which Britain would retain European Union rules and so avoid border problems with Ireland, could be extended by a year to 2021.
The summit continues Thursday with an agenda limited to some issues both sides firmly agree on, including fighting cybercrime and dealing with an assertive Russian Federation.