Officials from both sides are meeting in Brussels, but chief EU negotiator Michel Barnier and British counterpart David Davis are not attending the start, underscoring low expectations for the talks, AFP reported.
This round of divorce discussions is the last before European leaders meet at a summit on October 19 to decide whether there is "sufficient progress" to move on to the trade talks that Britain desperately wants.
The European Commission roundly rejected May's assertion that it was up to Brussels to take the initiative to advance the stalled talks, amid fears that her domestic political woes were threatening the negotiations.
"We do not provide comment on comments but what I can remind you of is there is a clear sequencing to these talks and there has been so far no solution found on step one, which is the divorce proceedings," the commission's chief spokesman Margaritis Schinas told a press conference.
"So the ball is entirely in the UK court for the rest to happen," he added.
Even before the commission's latest intervention, the prognosis for the talks was grim, with European Commission chief Jean-Claude Juncker having warned that "miracles" would be needed this week to make enough progress to get a positive decision at the summit.
Brussels is particularly alarmed by the leadership crisis engulfing the British prime minister, facing a plot to oust her after a catastrophic, mishap-strewn speech at her Conservative Party's conference.
The embattled May is set to tell the British Parliament on Monday that she expects "leadership and flexibility" from the other 27 EU countries in the negotiations.
"As we look forward to the next stage, the ball is in their court. But I am optimistic we will receive a positive response," May was expected to say, according to her office.
"I believe we can prove the doomsayers wrong."
Barnier and Davis are expected to give a press conference on Thursday after four days of talks, although officials added that was yet to be confirmed. Wednesday's timetable remains empty for now.
The questions over May's leadership have seriously damaged hopes that a speech she gave in Florence in September, which contained key concessions, could give a "new dynamic" to the talks.
The talks have stalled on all three of the key divorce issues –
the exit bill Britain must pay, the rights of EU citizens living in Britain and the fate of the border between Northern Ireland and Ireland.
London wants to begin talks on the future, including a possible EU-UK trade deal, as soon as possible.