Martin Schulz told German newspaper Bild am Sonntag that a period of limbo over Brexit would "lead to even more insecurity and thus endanger jobs".
"Hesitating simply to accommodate the party tactics of the British conservatives hurts everyone," he said.
"That is why we expect the British government to now deliver. The summit on Tuesday is the right time."
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.
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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 negotiations on the so-called "Brexit" 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 EU will hold a summit 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 yesterday urged Britain to begin the exit process "as soon as possible".