After another inconclusive negotiating session, both sides said differences remained on vital divorce issues including Britain's Brexit bill, the Irish border and the rights of citizens affected by Brexit.
EU leaders are due to assess at a Dec. 14-15 summit whether "sufficient progress" has been made on divorce terms to move to phase two of the talks, as Britain desires.
EU chief negotiator Michel Barnier confirmed that means Britain needs to make a shift within two weeks to give the 27 other EU leaders time to assess things before their December meeting.
The biggest stumbling bloc remains money. Britain has said it will pay to settle commitments it has made to the EU budget, but has not agreed to the EU's estimated bill of some 60 billion euros ($70 billion).
Barnier said it was "imperative" to turn into concrete commitments May's promise that Britain will pay its financial dues before leaving the EU on March 29, 2019.
In a recognition that progress has been slow, U.K. Brexit Secretary David Davis said that "we need to see flexibility, imagination and willingness to make progress on both sides if these negotiations are to succeed."
In Berlin, Steffen Seibert, spokesman for Chancellor Angela Merkel said Friday that "it is indeed in Great Britain's hands to create the conditions that would make it possible" to move to the next phase of trade relations.
May faces a multitude of woes on the domestic front, including a minority government deeply divided over Brexit, a sexual harassment scandal involving a growing number of politicians and resignation of two Cabinet ministers so far this month.
Asked whether the EU worries May's government might collapse, Barnier said "I am not going to comment on the internal political situation in the United Kingdom."
"We are, of course, watching it very closely," he added.
May faces another test when a key piece of Brexit legislation, the EU Withdrawal Bill, returns to the House of Commons next week. Pro-EU lawmakers say they will try to amend it to give Parliament a veto on any deal with the bloc.
Trying to regain a grip on the Brexit process, May warned pro-EU legislators they must not try to slow or stop the country's departure.
May said in The Daily Telegraph newspaper that the government would not tolerate attempts "to try to block the democratic wishes of the British people by attempting to slow down or stop our departure from the European Union."
The comments came as the official who created the rules for leaving the EU said that Britain can legally stop the process any time it wants before exit day in 2019.
John Kerr, who drafted Article 50 of the EU's key treaty, said that "while the divorce talks proceed the parties are still married ... We can change our mind at any stage."
Kerr said the British government has misled voters into believing the process is unstoppable.
The government said it plans to enshrine in law the date and time of the U.K.'s departure - 11 p.m. on March 29, 2019 - as a protection against delay.
Lawless reported from London. Frank Jordans in Berlin contributed to this story.
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