The chairman and ranking member of the House Oversight Committee called on Secret Service Director Kimberly Cheatle to resign in a rare bipartisan joint statement on Monday, following hours of questioning the agency director.

Following six hours of testimony in which Ms. Cheatle was asked numerous questions from both Republicans and Democrats about the assassination attempt on former President Donald Trump in Pennsylvania earlier this month, committee chairman Rep. James Comer (R-Ky.) and ranking member Rep. Jamie Raskin (D-Md.) said they both believe it’s time for her to step down.

In a letter to Ms. Cheatle, they said she “failed to provide answers to basic questions regarding that stunning operational failure and to reassure the American people” that the agency can move forward after the July 13 shooting that left former President Trump’s ear injured, one person dead, and two wounded.

“In the middle of a presidential election, the Committee and the American people demand serious institutional accountability and transparency that you are not providing,” the two said in a statement. “We call on you to resign as Director as a first step to allowing new leadership to swiftly address this crisis and rebuild the trust of a truly concerned Congress and the American people.”

Both Republican and Democrat lawmakers during the hearing suggested that Ms. Cheatle resign.

But she repeatedly rebuffed calls to leave her post, saying at one point early in the hearing: “I think that I am the best person to lead the Secret Service at this time.”

“Do you really, genuinely, in your heart, believe that you being in this role is what’s right for America at this moment?” Rep. Ro Khanna (D-Calif.) asked.

“I will remain on, and be responsible to the agency, to this committee, to the former president, and to the American public,” Ms. Cheatle replied, noting her 27-year record working up the agency’s ranks.

Monday’s hearing marked the first round of congressional oversight of the attempted assassination at an outdoor campaign rally that raised questions about the agency’s ability to protect current and former presidents. The suspected shooter, 20-year-old Thomas Matthew Crooks, was shot and killed by a Secret Service sniper moments after he opened fire.

Mr. Crooks was able to shoot at the former president and other rally-goers from about 400 feet away while perched atop a building. Ms. Cheatle was asked multiple times about why there was no agent placed on the building, but she did not answer the questions directly, citing ongoing investigations.

The Secret Service director last week told CNN that an agent was not put on the roof that Mr. Crooks had used because it had sloping features and posed a safety risk.

In the face of lawmakers’ claims that the Secret Service denied resources to protect former President Trump, Ms. Cheatle said security for the former president had grown ahead of the shooting. “The level of security provided for the former president increased well before the campaign and has been steadily increasing as threats evolve,” she said.

She added that the Secret Service provided the security sought by the Trump campaign for the rally.

During the hours of questioning, the agency director would not directly answer questions from both Republicans and Democrats about the security perimeter of the rally, if the agency knew of possible threats ahead of time, and eyewitness accounts of the suspect’s suspicious behavior before the assassination attempt.

Ms. Cheatle said she wanted to provide information but cited multiple ongoing investigations, including an internal probe due to be completed within 60 days. Lawmakers of both parties rejected the idea of a 60-day delay and accused her of stonewalling Congress.

In prepared remarks before the questioning, Ms. Cheatle said the shooting in Pennsylvania was “the most significant operational failure at the Secret Service in decades” and also the worst moment for the Secret Service since the attempted assassination of President Ronald Reagan in 1981.

Several Democrat lawmakers also asked whether more stringent gun-control laws would have prevented the shooting. Ms. Cheatle did not directly comment on the issue of guns, saying that the agency backs Americans’ Second Amendment rights.

“The job of the Secret Service is difficult every day,” Ms. Cheatle said at one point, adding that gun laws are different in every state and jurisdiction and that the agency has to prepare for that.

On Wednesday, FBI Director Christopher Wray will appear before the House Judiciary Committee. House Speaker Mike Johnson (R-La.) said he would unveil a bipartisan task force for a multitude of House investigations.

Reuters contributed to this report.