On a charm offensive with key leaders, May flew first to Berlin to plead for good terms with German Chancellor Angela Merkel, and then set off for Paris for an encounter with President Emmanuel Macron, seen as her counterpart with the toughest demands.
"France is really trying to play bad cop here," said Larissa Brunner, an analyst at European Policy Centre, referring to French insistence that another extension to her deadline must come with strings attached and assurances from London.
However, an official in Macron's office said that France was ready to accept a new delay.
While Macron still has a long list of conditions, it was a notable shift in France's tone compared to last week.
The reason for the change was unclear, though concerns have been growing about how badly a hard Brexit would hit the French economy, too. France was also encouraged by May's outreach last week to Britain's political opposition to find a compromise, and Macron may have been swayed in part by a meeting with the Irish prime minister.
France, which has had a love-hate relationship with Britain for about 1000 years, is now at the forefront to get the EU to take some decisive action.
"We won't be able to perpetually live with the exit of Brexit," French Foreign Minister Jean-Yves Le Drian said over the weekend. "At some point there is an exit."
Germany thinks likewise. "There isn't an endless readiness to keep talking about delays so long as there is no substantial progress on the British side," said Michael Roth, Germany's deputy foreign minister.
All eyes are now turned toward Macron, who has it in his power to force Britain to choose between a no-deal Brexit and cancelling its departure altogether. A drastic cliff-edge departure would have huge costs to businesses and trade across the English Channel and be very cumbersome to travellers as it would hit airports, ports, tariff rules and standard regulations overnight.
EU rules say that any extension to the Brexit deadline needs unanimity among the 27 other member states, and even if smaller member states would be hard-pressed to do it on their own, France has never shied away from being an EU leader — even at the expense of Britain.
Among conditions France is now setting to agree to a new delay: A "credible prospect" of some kind of solution to the British political deadlock. A promise that Britain won't keep asking for more delays. And guarantees that Britain would not be involved in future EU decisions while its Brexit drama is playing out.
"The longer the extension might be, the more guarantees are needed," a French official said.
Britain's Byzantine parliamentary disarray that has left Brexit in a state of a flux has added to continental annoyance.
"We are in a very, very frustrating situation here," Roth said as he arrived at an EU meeting in Luxembourg. But, he added, a disorderly Brexit would be "the worst of all options on the table."
"So far absolutely nothing has changed," Roth said. "Within the European Union, there isn't an endless readiness to keep talking about delays so long as there is no substantial progress on the British side."
Several days of talks between May's Conservative government and the main opposition Labour Party tried to find a compromise Brexit deal have failed to produce a breakthrough. Labour favours a softer Brexit than the government has proposed, and wants to retain a close economic relationship with the bloc.
After further talks, the two sides said they would resume their discussions after the EU summit.
May's Downing Street office said the talks had been "productive and wide-ranging." Labour business spokeswoman Rebecca Long-Bailey said there had not been "any fundamental shift ... but we're hopeful that progress will be made."
- AP
