Mr. Kuczinski said he never listened to the recorded calls himself. Instead, he said, he assigned two members of his staff to investigate, but because of the demands of his new role, it took him two weeks to do so. It took the staff members several weeks to review the recordings and conclude that the calls did not indicate an attempt to frame anyone, he said. He said he did not initially notify the Department of Investigation about the matter in February because he believed it would have posed a conflict for the agency.

Image Gregory Kuczinski Credit... City of New York Department of Corrections

Mr. Ponte defended Mr. Kuczinski, affirming Mr. Kuczinski’s assertion that he was not initially involved with the call monitoring unit that had picked up the conversation between the Department of Investigation employee and an inmate informant. Mr. Ponte acknowledged that better communication with the Department of Investigation could have prevented the monitoring of the investigator’s calls, but he placed some of the blame on the investigation agency.

“There are ways that D.O.I. could have told us that, these numbers, don’t listen to them,” he said.

The hiring of Mr. Kuczinski at the Correction Department remains something of a mystery.

As the deputy commissioner in charge of the agency’s Investigation Division, he is responsible for uncovering administrative misconduct in the ranks of the department’s 10,000 officers and investigating crimes committed by inmates.

But when he joined the jail agency in March 2015 as the division’s No. 2 official, Mr. Kuczinski, a retired New York Police Department sergeant and a lawyer, had little investigative and no internal affairs experience from his police tenure. Nonetheless, Mr. Ponte promoted him to the division’s top position about a year later, just days after he was rebuked and fined $1,500 for assigning an on-duty subordinate to drive him and his family to the airport for a summer vacation.

Officials at City Hall, the Department of Investigation and the Correction Department could not explain how Mr. Ponte came to hire and then promote Mr. Kuczinski despite his limited relevant experience. Mr. Kuczinski said he was hired after responding to a newspaper advertisement.

The investigation agency did not conclude that the spying was undertaken because of the report on vehicle misuse, the people with knowledge of the letter said. But the letter “did note concerns of the timing of certain actions regarding monitoring of D.O.I. investigator phone calls, especially at the direction of Kuczinski, that immediately followed D.O.C. being notified about the vehicle investigation,” one of the people said.