Gunther Oettinger called on the PM to “lead” and defy hard Brexiteers in her party in a series of unguarded remarks.
He also described solving the Irish border as “mission impossible” just as British and European negotiators looked poised to seize a breakthrough.
Mr Oettinger, who is a close ally Angela Merkel, made the remarks during a speech in Brussels this week.
He said: “The most important thing was that Mrs May — with or without dances — left her party conference strengthened, er, she survived.
“She must now use the momentum. She must now lead and be prepared to make further concessions to us, no matter what Boris Johnson thinks or says.”
The gaffe-prone German official blundered into the talks at a delicate time, with officials having entered a period of radio silence dubbed “the tunnel”.
His speech came as the leaders of Germany and the Netherlands hailed significant recent progress in the negotiations.
Mrs Merkel said there was a good chance to “log a result” at next week’s crunch EU summit with talks now at a “very, very intensive” pace.
She said: “We’re going on the principle that the faster we’re done, the better. It’s important that we can really log a result next week.
“Apparently progress has been made, but sometimes the devil is in the details.
“A solution is only possible if everything has been resolved, and if we make more progress next week, that’s a good signal.”
And Mark Rutte described himself as “cautiously optimistic” that a deal can be sealed within the next few days of talks.
Following a meeting between the pair in The Hague, the Dutch PM added: “A lot depends on the talks in the coming days.”
But hopes a Brexit deal can be sealed next Wednesday were dashed after eurocrats said there has been “no breakthrough” in the talks.
Michel Barnier was reported to have said a pact was “within reach” during a keynote address at the EU Parliament on Wednesday night.
But EU sources blamed a faulty translation for the misunderstanding, which had caused the pound to surge amid misplaced optimism.
A Commission spokesman said: “Today we are not there yet. There is no breakthrough yet.
“Intensive technical negotiations are continuing to see if we can reach decisive progress. We’re working hard to reach a deal.”
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