The European commission president, Jean-Claude Juncker, has called on the UK to "stop wasting time" and insisted Brexit cannot continue to be delayed indefinitely.
Britain's departure from the bloc has already been delayed twice, with it first pushed back to April 12, before a decision to extend the delay until October 31 was agreed.
"I hope that the British will make use of this time and not waste it again. We cannot keep on putting off the withdrawal date indefinitely," Juncker said.
"The best solution would be for the British to adopt the withdrawal agreement during the extra time that has been agreed."
May was able to gain support for her six-and-a-half month delay from all 27 EU member states earlier this month as she tries to find a way to get a withdrawal agreement through Parliament.
Juncker told German newspaper, FUNKE Mediengruppe, that a no-deal Brexit was still a real possibility, however.
"Nobody knows how Brexit will end. This is creating great uncertainty. There is still a fear that there will be a hard Brexit without any withdrawal treaty arrangements," he added.