WASHINGTON — An armed man who jumped the White House fence this month made it far deeper into the mansion than previously disclosed, overpowering a Secret Service agent inside the North Portico entrance and running through the ceremonial East Room before he was tackled, according to a member of Congress familiar with the details of the incident.

The man, Omar J. Gonzalez, who had a knife, was stopped as he tried to enter the Green Room, a parlor used for receptions and teas, said the congressman, Representative Jason Chaffetz of Utah, the Republican chairman of a subcommittee looking into the security breach. Earlier, Secret Service officials indicated that Mr. Gonzalez, 42, had only made it steps inside the North Portico after running through the door.

The new development, first reported by The Washington Post, raised immediate questions about whether the Secret Service had been forthright in its initial accounts of the episode. It will set the stage for an explosive congressional hearing on Tuesday when lawmakers say they intend to grill Julia Pierson, the director of the Secret Service, about whether an undisciplined culture inside the long-heralded agency has eroded its ability to protect the president and his family.

The hearing is set to focus on a series of security embarrassments over the last several years, including a breach that occurred when a couple crashed a state dinner in 2009, a 2011 incident when bullets struck the White House, scandals involving drinking and prostitution on overseas trips in 2012 and 2013, and 16 separate cases of people scaling the White House fence in the last five years. Ms. Pierson became director in 2013.