Amid confusion and dissent over the timetable for any "Brexit", Martin Schulz told German newspaper Bild am Sonntag that a period of limbo would "lead to even more insecurity and thus endanger jobs".
"Hesitating simply to accommodate the party tactics of the British Conservatives hurts everyone," Schulz, a German Social Democrat, said.
"That is why we expect the British government to now deliver. The summit on Tuesday is the right time."
However German Chancellor Angela Merkel's chief of staff insisted there was no rush to show Britain the door.
"The political leadership in London should have the chance to reconsider once again the consequences of a withdrawal," Peter Altmaier told the RND media group.
He noted that once Britain left the union, it would be a "serious turning point with many consequences".
Altmaier had earlier told German public radio that he had "no indication" that British Prime Minister David Cameron would start the Brexit process Tuesday.
"I tend to think that the application will be filed in the coming weeks or months, possibly only by a new government," he said.
After it has been formed, the new British government will "then sort itself out and, as the case may be, present its application. We should all wait calmly for that".
However the four biggest groups in the European Parliament have also drawn up a draft resolution calling for Cameron to set the Brexit ball rolling on Tuesday, Germany's Frankfurter Allgemeine Sonntagszeitung reported.
This was crucial, the groups wrote, "to avoid damaging uncertainty for all and to preserve the integrity of the union".
They added that "no new relationship of whatever kind between the United Kingdom and the EU can be agreed before (Britain's) exit accord has been completed".
Cameron said Friday in the wake of the shock referendum outcome favouring Britain leaving the EU that he would resign his office by October and leave the Brexit negotiations to his successor.
To begin the withdrawal process, Britain must invoke Article 50 of the EU's Lisbon treaty, which has never been used before.The first step is to inform the European Council of member states, which sets the clock ticking on a two-year timetable of negotiations.
The EU will hold a summit in Brussels Tuesday and Wednesday to discuss the fallout from the British vote and the European Parliament will also hold a special session.
Foreign ministers from the EU's six founding states meeting in Berlin on Saturday urged Britain to begin the exit process "as soon as possible".
Merkel, however, was more cautious, saying it was up to Britain to decide when to begin withdrawal proceedings, although they should not "drag on forever".
"There is no reason to be nasty in the negotiations. We have to follow the rules of the game," she said.