A written summary of the internal investigation into Mr. Coleman provided to The New York Times redacted the name of the target of the inquiry, but said the person had “engaged in serious misconduct and mismanagement” that created a “‘toxic’ workplace culture.”

A FEMA spokeswoman, Jenny Burke, said the agency would not comment beyond Mr. Long’s statement because the investigation was continuing.

Attempts to reach Mr. Coleman were not successful on Monday.

The summary said an investigator had contacted 73 witnesses and taken 98 statements after the allegations of misconduct emerged. The inquiry found that Mr. Coleman had circumvented his office’s management structure in order “to concentrate unquestioned authority in himself” and intimidate “any subordinates who might question his decisions,” according to the summary.

The summary found that Mr. Coleman had sexual intercourse with one woman in 2015, while the woman was his subordinate. Mr. Coleman also made sure the woman was assigned to work directly with him; pressured her to go on dates; and the woman was at one point denied a promotion after she refused Mr. Coleman’s advances, the summary said. The woman told the investigator that she kept her job by telling Mr. Coleman that she might be willing to go on dates with him again, the summary said.

The investigation also found that Mr. Coleman had a second inappropriate relationship with a separate female subordinate in 2017 and 2018. He allowed the woman to work from his home and made her accompany him on official travel even though she was given few responsibilities. When the woman said she wanted to leave FEMA, he created a job for her — even though she was not qualified for it — and paid for it with disaster funding, the summary said.

Finally, the investigation found that Mr. Coleman had granted an unfair advantage when he hired a fraternity brother in 2014 for a job the man was not qualified for.

Mr. Long said that as a result of the initial investigation, he had ordered the officials to establish an Office of Professional Responsibility that would handle allegations of employee misconduct. He also has ordered a third-party review of how the agency handles such complaints; counseling services for FEMA employees; and mandatory training aimed at preventing sexual harassment.

Officials said Mr. Coleman came to FEMA in 2011 as deputy personnel chief and was later promoted.

“We — as an agency — have a lot of work to do,” Mr. Long wrote in his email to employees, “especially with respect to sexual harassment in the workplace.”