ABC Exclusive: Trump rally shooting 'unacceptable,' Secret Service ...

In her first network interview since the assassination attempt on former President Donald Trump, U.S. Secret Service Director Kimberly Cheatle said that the Pennsylvania rally shooting was "unacceptable."

"It was unacceptable," she said in an interview Monday with ABC News Chief Justice Correspondent Pierre Thomas. "And it's something that shouldn't happen again."

The violent incident on Saturday, which left one rallygoer dead, marked the first time a current or former president has been wounded in an attempted assassination since Ronald Reagan in 1981.

When she first learned of the shooting, Cheatle said she was shocked and concerned -- both for Trump and for the Secret Service agents who responded to the incident.

"It was obviously a situation that as a Secret Service agent, no one ever wants to occur in their career," she said.

As the head of the agency, Cheatle said it's her responsibility to investigate what went wrong and make sure nothing like it can happen again.

TIMELINE: How the Trump assassination attempt unfolded at rally in Pennsylvania

"The buck stops with me," she said. "I am the director of the Secret Service, and I need to make sure that we are performing a review and that we are giving resources to our personnel as necessary."

Cheatle responded to reports that the suspect was seen and identified as potentially suspicious before he opened fire, saying that "a very short period of time" passed between then and the shooting.

"I don't have all the details yet, but it was a very short period of time," she said. "Seeking that person out, finding them, identifying them, and eventually neutralizing them took place in a very short period of time, and it makes it very difficult."

Cheatle also said that local authorities were tasked with securing the building where the alleged shooter fired the shots before being taken out by a Secret Service sniper, and confirmed that local police were present inside the building while the shooter was on the roof.

"In this particular instance, we did share support for that particular site and that the Secret Service was responsible for the inner perimeter," Cheatle said. "And then we sought assistance from our local counterparts for the outer perimeter. There was local police in that building -- there was local police in the area that were responsible for the outer perimeter of the building."

MORE: : Investigation into Trump assassination attempt focuses on motive

Cheatle said she has reached out to Trump but has not yet spoken with him.

In the days since the attack, Cheatle and the Secret Service have faced heightening scrutiny for failing to prevent the incident from happening, and even calls from some to resign.

Cheatle said she would not resign from her role.

She is expected to testify before the GOP-led House Oversight Committee next Monday, July 22.