WASHINGTON — Senators investigating the Secret Service prostitution scandal said Wednesday that dozens of reported episodes of misconduct by agents point to a culture of carousing in the agency and urged Director Mark Sullivan to get past his insistence that the romp in Cartagena was a one-time mistake.

The disconnect between the senators and Sullivan reappeared again and again during the two-hour hearing, even as the Secret Service chief for the first time apologized for the incident that tarnished the elite presidential protection force.

By the end, Sullivan’s job appeared secure even as new details emerged that left little doubt, senators said, that a pattern of sexual misbehavior had taken root in the agency.

“He kept saying over and over again that he basically does think this was an isolated incident, and I don’t think he has any basis for that conclusion,” said Sen. Susan Collins of Maine, the senior Republican on the Homeland Security panel that heard Sullivan’s first public accounting of the episode.

“For the good of the Secret Service,” added Sen. Joe Lieberman, I-Conn., the panel chairman, “he’s got to assume that what happened in Cartagena was not an isolated incident, or else it will happen again.”

Sullivan insisted repeatedly that in his 29-year Secret Service career, he had never heard anyone say that misconduct was condoned, implicitly or otherwise.

“I just do not think that this is something that is systemic within this organization,” Sullivan said.

The misconduct became public after a dispute over payment between a Secret Service agent and a prostitute at a Cartagena hotel on April 12. The Secret Service was in the Colombian coastal resort for a Latin American summit before President Barack Obama’s arrival.

Twelve employees were implicated; eight of them were ousted, three were cleared of serious misconduct and one is being stripped of his security clearance. Sullivan said two who initially resigned now are fighting for their jobs back.

“These individuals did some really dumb things,” Sullivan told the Senate panel. “I’m hoping I can convince you that it isn’t a cultural issue.”

He didn’t make much progress on that front, as senators offered fresh evidence of what they considered reckless behavior. Lieberman said 64 allegations or complaints of sexual misconduct were made against Secret Service employees in the last five years.

Three of those, Lieberman said, were complaints of inappropriate relationships with a foreign national and one of “nonconsensual intercourse,” on which he didn’t have enough information to elaborate.

Sullivan said that complaint was investigated by outside law enforcement officers, who decided not to prosecute.