The remains of every U.S. military member killed overseas are flown to Dover for processing. Family members attend the arrival, but the secretary of defense usually does not.
The Pentagon did not announce Hagel's visit, but an official who confirmed it said Hagel planned to meet privately with members of the families of the four soldiers. The official spoke on condition of anonymity because he was not authorized to discuss the matter publicly.
The four soldiers killed Sunday are 1st Lt. Jennifer M. Moreno, 25, of San Diego, Calif.; Sgt. Patrick C. Hawkins, 25, of Carlisle, Pa.; Sgt. Joseph M. Peters, 24, of Springfield, Mo., and Pfc. Cody J. Patterson, 24, of Philomath, Ore.
In a statement Tuesday, U.S. Army Special Operations Command said Hawkins and Patterson were members of the 3rd Battalion, 75th Ranger Regiment, and Peters was a special agent assigned to the 286th Military Police Detachment.
Moreno was working with the other three on a joint special operations task force in southern Afghanistan as a cultural support officer. She was assigned to Madigan Army Medical Center at Joint Base Lewis-McChord, Wash.
The Pentagon said Tuesday that during the first week of the partial government shutdown, 17 military members died at home and abroad. They include Marine Lance Cpl. Jeremiah M. Collins, Jr., 19, of Milwaukee, Wis., who was killed Saturday in Afghanistan. None of their families has received the $100,000 emergency payment.
The administration has been criticized by some members of Congress for suspending the emergency death payments to families of those killed. The Pentagon says payments are not legally allowed during the government shutdown.
Rep. Duncan Hunter, R-Calif., wrote to Hagel on Tuesday complaining about the suspension of the $100,000 death benefit and accusing the Pentagon of making that decision on the basis of a "careless legal interpretation."
Administration officials have said the decision was based on a legal review by government lawyers, including the Justice Department. Congress is considering legislation that would authorize restoring the suspended death payments.