ISTANBUL—President Recep Tayyip Erdogan on Thursday called on Turkey’s political leaders to form a government as soon as possible, ending an unusually long public silence after Sunday’s elections delivered the country’s first hung parliament in more than a decade.

“A government should be formed immediately under the constitutional framework, with the understanding that continuity is fundamental to the state,” Mr. Erdogan said at a graduation ceremony for international students in Turkey organized by the Ankara Chamber of Commerce....