City officials covered up nearly 120 “serious incidents” at homeless shelters by downgrading their severity so they wouldn’t have to be disclosed to state regulators, according to the city Department of Investigation.

The DOI conducted a yearlong probe into allegations that the Department of Homeless Services wasn’t “adequately” reporting arrests and other problems to the state Office of Temporary and Disability Assistance, which is responsible for ensuring that shelters are safe.

The investigation revealed that DHS created its own “priority codes” that minimized “life-threatening injuries,” mental-health emergencies and some arrests of residents, visitors or staffers, according to an April 8 DOI memo obtained by The Post.

There were “approximately 117 internal reports” from January through June 2017 that contained information that should have been reported, the memo said.

City Councilman Ritchie Torres (D-The Bronx), who tipped off DOI to the situation, told The Post, “There’s only one word for the conduct of DHS: inexcusable.”

“DHS adopted a dubious definition of serious incidents that it knew would lead to the under-reporting of incidents consisting of serious injuries, mental health emergencies, arrests and situations affecting the safety of its own residents and staff,” Torres said.

“I am committed to introducing legislation that would end, once and for all, the semantic gamesmanship around critical incident reporting.”

Midway through the DOI probe, DHS gave the state all the reports in question and also hired seven staffers to ensure incidents get properly reported, according to the memo.

City Hall spokeswoman Freddi Goldstein said, “The issues raised in this report are two years old and … have been addressed.”

Additional reporting by Bruce Golding