Britain’s Prime Minister Theresa May speaks to the media after she arrives at the European Council for the start of the two day EU summit on December 13, 2018 in Brussels, Belgium.

"The Union stands by this agreement and intends to proceed with its ratification. It is not open for renegotiation," the statement said Thursday.

However, while EU leaders agreed to write a joint statement after discussing the latest Brexit developments, they did not change their position on U.K.'s withdrawal agreement from the EU.

Ahead of the EU summit, May admitted she was not expecting an "immediate breakthrough." Instead, she hoped both sides could revisit British lawmakers' Irish backstop concerns to improve the chances of getting her Brexit deal through the Parliament.

The prime minister was hoping to get "legal and political" reassurances from the other 27 member countries regarding the Irish backstop — the biggest stumbling block preventing progress in the Brexit process.

Britain's embattled Prime Minister Theresa May will go back to London empty-handed on Friday, after racing to Brussels to try to get a few more concessions from the European Union.

The EU-27 also said it stands ready to start negotiations on future trade arrangements as soon as the U.K. leaves in March. They also repeated the Irish backstop is only an insurance policy.

"It is the Union's firm determination to work speedily on a subsequent agreement that establishes by 31 December 2020 alternative arrangements, so that the backstop will not need to be triggered," the 27 countries said.

The EU added that if the Irish backstop policy needed to be triggered, it would only apply "temporarily" until there's an agreement in place.

The idea of the backstop is to prevent a hard border between Northern Ireland and Ireland — a critical issue for both the EU and the U.K.

Brexiteers and other U.K. lawmakers believe this plan forces Northern Ireland to follow EU rules. However, both Westminster and the EU have said this would not be their aim and if it were to happen, it would only apply until they implement new trade arrangements.

"There will be no new legally binding obligations imposed on the European Union. That's crystal clear," European Commission President Jean-Claude Juncker told reporters in Brussels Thursday night.

The U.K. Parliament is legally scheduled to vote on the withdrawal agreement before January 21.

Meanwhile, Luxembourg Prime Minister Xavier Bettel told CNBC in Brussels that it is time for U.K. lawmakers "to be responsible."

"Theresa May did the best possible deal and now MPs in London should be responsible and to know if they want to have the best possible deal or want to go in the direction where they don't know what will come out," he said.

"It's in the interest of their citizens," he added.

Sterling was down 0.6 percent against the dollar at $1.2591, with Reuters citing May's unsuccessful Brexit trip to Brussels. The British currency also dropped 0.3 percent versus the euro to 90.025 pence.