'City of David' in the Bible

Shallun son of Col-hozeh, ruler over the district of Mizpah, repaired the Fountain Gate. He rebuilt it and roofed it. Then he installed its doors, bolts, and bars. He also made repairs to the wall of the Pool of Shelah near the king’s garden, as far as the stairs that descend from the city of David.

At the Fountain Gate they climbed the steps of the city of David on the ascent of the wall and went above the house of David to the Water Gate on the east.