Manfred Weber, an ally of Angela Merkel, posted a video to Twitter expressing the need for the UK to come to the next round of exit talks with “very concrete proposals”.
He insisted the EU27 already knew what it wanted from negotiations with the UK during the call for “clarity”.
He said: “The speech of Theresa May in Italy was positively received, but it was again without further substance, with more details.
“What we expect now is that in the next round of negotiations we now need substance, we now need very concrete proposals from the British side.
“Europe knows what we want to achieve, and now it’s up to Britain to clarify what they want to achieve.”
The comments come after he tweeted he was “even more concerned” about Brexit directly after the Prime Minister’s speech.
Mr Weber, an MEP and member of Germany’s Christian Social Union, also warned Britain “the clock is ticking” in a series of provocative posts on Britain’s EU exit.
He said: “In substance Prime Minister May is bringing no more clarity to London’s positions. I am even more concerned now.
“The clock is ticking and time is running faster than the government believes in London.”
He said, while the economic impact of Brexit was important, the rights and security of EU citizens in Britain held more weight.
Mr Weber posted: “Money is one thing but people’s everyday life is more important. EU citizens in the UK need legal certainty.”
The status of EU citizens is one of the three red-line issues, along with the future of the Irish border and an EU divorce fee, holding up Brexit talks.
Mrs May addressed two of these topics during her speech this afternoon – albeit in both cases with little concrete detail.
While she rejected the possibility of “physical infrastructure” on the Irish border, Mrs May failed to explain how customs could be enforced on its 300 road crossings or how to reconcile the issue of thousands of fields, properties and buildings which straddle the invisible divide.
And she conceded Britain would pay what it owed to the EU but dodged requests for clarification on what sort of figure she saw as acceptable.