WASHINGTON — Members of Congress declared Tuesday that they had lost confidence in the Secret Service to protect President Obama and his family and raised serious doubts that Julia Pierson, the director of the agency, was the right person to confront what they called systemic problems and a striking lack of candor about recent security breaches.

After three hours of combative questioning by members of a House panel, lawmakers from both parties called for an independent investigation of a bureaucracy they said could no longer police itself and was endangering the very people it is sworn to protect.

Ms. Pierson defended her agency, but she repeatedly acknowledged that “mistakes were made” by agents and officers as they ignored standard protocols for responding to threats. Notably, Ms. Pierson did not explain why Secret Service officials initially misled the public about how far inside the White House an armed intruder, Omar J. Gonzalez, managed to get on Sept. 19.

Officials originally said Mr. Gonzalez was unarmed and had been captured just inside the door of the North Portico, but later acknowledged that the intruder had carried a small knife and made it through the Entrance Hall and the Cross Hall and into the East Room before being tackled just outside the Green Room.