The European Union agreed to postpone the United Kingdom's exit from the bloc, but the length of the delay will depend on whether or not the British parliament accepts the previously negotiated withdrawal agreement.
European Council President Donald Tusk said the bloc would grant an extension until May 22 if Prime Minister Theresa May is able to convince the British parliament to accept the existing Brexit deal.
If May is unable to convince parliament, which has previously rejected the deal, then Britain would face a disorderly exit from the European Union on April 12.
May had asked Brussels for the March 29 Brexit date to be delayed three months until at least June 30. The British parliament has twice rejected the withdrawal agreement that she had negotiated with the European Union, which has raised the prospect of a disorderly and economically damaging exit from the European Union.
Speaking to reporters, May said she believed the U.K. will absolutely eventually leave the EU.
"Yes, we will be leaving the European Union, and I absolutely fervently believe that it is the duty of Parliament to deliver on that result of the referendum," she said in response to a question about whether Brexit could be delayed further. "I also believe that it is better for the U.K. if we can do that with a negotiated deal, do that in a smooth and orderly manner. That's what tonight's decision from the Council enables us to do."
The prime minister emphasized that Parliament needs to resolve the situation: "We are now at that moment of decision."
"There was a clear result that we should leave the European Union," May added. "We said, 'Here's the vote, what is your decision? And we will deliver on it.' And I believe it is out duty as a government, as a Parliament to deliver on that vote."
Those assurances come after the U.K. Parliament's petitions website crashed on Thursday as calls to revoke Article 50 and overturn Brexit quickly exceeded 1 million signatures. Just before midnight that day, the number of signatures had already topped 2.1 million.
The House of Commons Petitions Committee said in a Thursday Twitter post it was seeing the highest rate of signing that any petition on its site had ever had, adding that changes had been made to its website to deal with the traffic influx. According to the Parliament website, lawmakers would consider the petition for debate if it surpassed 100,000 signatures.
In her comments to reporters, May said British members of parliament will have a chance next week to look at the choices they face, adding that her team will need to work with Parliament on how to proceed if the current deal fails to pass.
—Reuters and CNBC's Chloe Taylor contributed to this report.