The two men left the jail by entering an administrative suite and breaking a window, according to Director of the D.C. Department of Corrections Devon Brown.
"This was not an easy task to accomplish," he said.
It was not clear why the two men were in that area of the jail.
The jail was put on lockdown after the escape.
An officer arriving for work unsuccessfully chased the two men, losing track of them in the area of a Metro Station not far from RFK Stadium.
The prisoners were last seen near the jail at 19th Street and Independence Avenue, SE. Police believe they rode a Metro shuttle bus to the Minnesota Avenue station in northeast Washington, Gentile said.
Both men were wearing blue prison jumpsuits at the time of their escape.
Metro is running a free shuttle every five minutes between the stadium stop and Minnesota Avenue because of track maintenance this weekend,
Jones and Leaks were both awaiting trial for a shooting last July in the District. Jones was charged with first-degree murder while armed in that case and Leaks was charged as an accessory in that case.
The two are also wanted in North Carolina for allegedly shooting a security officer in Greensboro, Gentile said.