Secret Service Director Julia Pierson admitted Tuesday that presidential security fell apart when a knife-wielding intruder jumped a White House fence earlier this month and sprinted untouched across the lawn, entering the first family's residence through an unlocked door and making his way into the East Room reception area.

Pierson testified at a House oversight hearing, her first since the Sept. 19 incident. She faced heated questioning from lawmakers who voiced deep skepticism about the state of the agency and the first family's safety. At the close of the public portion of the hearing, Chairman Darrell Issa, R-Calif., said an internal investigation is "not sufficient" and he would be working with colleagues to request an independent probe. 

The director, in her testimony, took "full responsibility" for the failures at her agency while challenging some of the lawmakers' tougher allegations about security. "The president is safe today," Pierson insisted. 

But she also faced accusations -- which she did not directly rebuff -- that the agency initially gave a "false" account of what happened that evening. 

In his opening statement, Issa noted that the knife-carrying intruder in fact made it to the East Room. Issa said that was contrary to an "early, false report" that claimed the intruder only got just inside the residence door. 

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"An intruder walked in the front door of the White House, and that is unacceptable. Commonsense tells us that there were a series of security failures -- not an instance of praiseworthy restraint," Issa said. He claimed the intruder breached at least five rings of security. Urging the Secret Service to fix its problems, he warned that the next breach could be a "planned attack by a terrorist organization." 

"The fact is, the system broke down," Issa said. 

Under questioning by Issa, Pierson acknowledged that the intruder "knocked back" an officer who was standing at the White House doorway, made it into the hallway and "stepped momentarily into the East Room." 

She said the intruder was handcuffed just outside a nearby room called the Green Room. (The Washington Post reported Tuesday that the individual who finally tackled the intruder was an off-duty agent who happened to be in the house and was leaving for the night.) 

The director also acknowledged that the outer glass "storm door" that the intruder entered through was not locked at the time. She said an auto-locking system has since been installed. 

Pierson faced bipartisan criticism over the security failures. Rep. Stephen Lynch, D-Mass., sharply challenged the director over how far the intruder penetrated the building. "To the American public, that would be half of a White House tour," he said. "This is disgraceful." 

He added: "I wish to God you protected the White House like you're protecting your reputation here today." 

In addition, House Homeland Security Committee Chairman Michael McCaul announced Tuesday that he is planning to introduce legislation for a blue-ribbon commission to conduct a probe of the agency.

"We need a comprehensive, independent assessment of the agency to ensure we have a Secret Service that can be trusted to fulfill and excel in its vital missions," McCaul, R-Texas, said.

In her opening statement, Pierson admitted that the security plan "was not properly executed." 

"This is unacceptable and I take full responsibility and I will make sure that it does not happen again," she said. She said all decisions from that day are being evaluated. 

The testimony comes after it was revealed Monday that the suspect in the Sept. 19 incident made it far deeper into the White House than previously known. 

Sources confirmed to Fox News that 42-year-old Omar Gonzalez overpowered a Secret Service officer and got all the way into the East Room before he was stopped.   

A series of what one source called "catastrophic" security failures apparently allowed the intruder to get that far.   

The Secret Service did not follow basic protocols during the incident to protect the White House, the president and the first family and the agency still does not know why, a source intimately familiar with details of the investigation told Fox News. 

For example, the Secret Service didn't lock down certain areas of the property and did not elevate the threat level at the White House so that other uniformed officers and agents would know what was happening, which is a standard response. 

"This was a catastrophic failure when the President was not there. What if the president was there?" the source, a longtime Secret Service insider, added. "It turns out that basic functions in place to avoid this were never initiated." 

The Secret Service has been having high-level meetings to address the breach, the latest in a series of embarrassing scandals for the agency since a 2012 prostitution scandal erupted during a presidential visit to Colombia. 

The Washington Post reported over the weekend that the Secret Service did not immediately respond to shots fired at the White House in 2011, amid what the agency describes as uncertainty about where the shots originated. Four days later, it was discovered that at least one of the shots broke the glass of a window on the third level of the mansion, the Secret Service said. 

At the time of the 2011 breach, the president and first lady Michelle Obama were away, but their daughters were in Washington -- one home and the other due to return that night. Oscar R. Ortega-Hernandez of Idaho has been sentenced to 25 years in prison for the 2011 incident. 

Gonzalez was on the Secret Service radar as early as July when state troopers arrested him during a traffic stop in southwest Virginia. State troopers there said Gonzalez had an illegal sawed-off shotgun and a map of Washington tucked inside a Bible with a circle around the White House, other monuments and campgrounds. The troopers seized a stash of other weapons and ammunition found during a search of Gonzalez's car after his arrest. 

The Secret Service interviewed Gonzalez in July, but had nothing with which to hold him. Gonzalez was released on bail. Then, on Aug. 25, Gonzalez was stopped and questioned again while he was walking along the south fence of the White House. He had a hatchet, but no firearms. His car was searched, but he was not arrested. 

"There's a misperception out there that we have some broad detention powers," Ed Donovan, a Secret Service spokesman, said. The Secret Service, like other law enforcement agencies, must have evidence of criminal behavior in order to file charges against someone. "Just because we have a concern about someone doesn't mean we can interview or arrest them or put them in a mental health facility," Donovan said. 

Fox News' Ed Henry and The Associated Press contributed to this report.