A joint statement issued after the talks in Brussels said Juncker had again warned that November's withdrawal agreement could not be renegotiated -- after May came hoping to persuade Brussels to agree on the need to change the so-called "backstop" clause for the Irish border.
But Juncker "expressed his openness to add wording" to a parallel political declaration laying out ambitions for future EU-UK ties if London wants to seek a "more ambitious" closer relationship after Brexit.
In a sharp reminder of the urgency of finding a solution before Brexit day on March 29, Bank of England governor Mark Carney warned that Britain's economy was "not yet prepared" for a no-deal departure.
May came hoping to change the backstop so that Britain cannot be "trapped" in the bloc against its will -- and by doing so win over enough MPs at home to get the deal through parliament.
She reminded Juncker that the British parliament had mandated her to seek "a legally binding change to the terms of the backstop", but instead was offered a fresh round of talks. EU negotiator Michel Barnier will now meet British Brexit Minister Stephen Barclay in Strasbourg on Monday.
May herself will meet Juncker again before the end of February, a commission spokesman said.
A stony-faced May shook hands stiffly with Juncker as she arrived at commission headquarters, refusing to answer questions, but she was expected to make a statement later Thursday.
Expectations for the visit were already modest when, on Wednesday, EU kingpins Donald Tusk and Juncker torched May's prospects of winning changes to the withdrawal agreement.
Juncker told reporters May already knows and accepts that the Union will not reopen talks on the deal, while Tusk, who represents EU member governments as head of the European Council, triggered outrage across the Channel by damning pro-Brexit politicians for -- in his view -- recklessly failing to plan.
"I've been wondering what that special place in hell looks like, for those who promoted Brexit without even a sketch of a plan how to carry it out safely," Tusk said.
- 'Don't gamble with peace' -
But even this latest demonstration of EU unity did not deter Downing Street, which insisted May's top priority on the trip was to "find a way to guarantee we cannot, and will not, be trapped in the backstop".
Number 10 said that because the British parliament rejected the deal, May must seek material changes to the accord or see it fail.
The impasse in Brussels has deepened fears that Britain could crash out of the EU without a deal on March 29, disrupting trade and supplies to manufacturing.
May has exasperated EU leaders by repeatedly coming to Brussels without detailed proposals to solve the Brexit deadlock, and Tusk warned her he expected her to bring "a realistic suggestion on how to end the impasse".
Jeremy Corbyn, the leader of the main opposition Labour party, wrote to May on Thursday setting out his five conditions for backing her on Brexit -- including the UK staying in the EU's customs union.
While his demands will not be palatable to many in May's Conservative party -- not least because of the deeply entrenched tribalism of British politics -- it suggests there may be room for manoeuvre, if not yet a clear path to a cross-party deal.
After seeing Tusk and Juncker on Thursday, May will have dinner with her Irish counterpart Leo Varadkar Dublin on Friday.
Varadkar, whose government has stressed the importance of maintaining an open border between Ireland and Northern Ireland after Brexit, said recent "instability in British politics" showed why a backstop was essential.
On Wednesday, May discussed the issue with Northern Irish leaders in the British province.
Last month, the House of Commons overwhelmingly rejected the Brexit deal that May had negotiated with the EU after 18 months of painstaking diplomacy.
May is now looking into changes to satisfy her MPs, who fear the backstop would keep Britain indefinitely tied to EU rules with even closer alignment for Northern Ireland.
May's spokesman stressed that she was not coming to Brussels to ask for more time and remained determined to deliver a Brexit deal before the March 29 deadline.
Juncker said again that the deal could not be renegotiated but he 'expressed his openness to add wording' to a parallel political declaration laying out ambitions for future EU-UK ties if London wants to seek a 'more ambitious' closer relationship after Brexit.