ISTANBUL—Turkish President Recep Tayyip Erdogan declared a three-month state of emergency in the southern areas hit by two powerful earthquakes that have killed more than 5,000 people and destroyed thousands of homes there and in northern Syria.

“The scale of the earthquake of course makes us take certain extraordinary measures,” Mr. Erdogan said Tuesday in a televised address. “We will be completing all the necessary procedures and formalities very fast.”