Detectives on Monday were seeking to verify the story of a South Side man who told police that the three people he shot dead inside his house were home invaders.

“We have noticed inconsistencies in his story . . . we’re pressing pretty hard,” police spokesman Anthony Guglielmi said Monday morning of investigators who were interrogating the man.

Police were investigating the shooting as self-defense. Area South detectives were conducting the homicide investigation.

Under mounting pressure, the man hired an attorney Monday afternoon, Guglielmi said.

No charges have been filed against the 31-year-old man, who has a valid Firearm Owner’s Identification card.

The shooting occurred about 5:32 p.m. in the basement of a home in the 10200 block of South Ewing in the East Side neighborhood, two blocks west of the Chicago Skyway.

Guglielmi could not immediately say what kind of gun police recovered from the man. Asked if the alleged intruders were also armed, he replied: “We only recovered one weapon.”

Two of those killed were identified by the Cook County medical examiner’s office as 22-year-old North Austin neighborhood resident Narcisco J. Ledesma, and 17-year-old East Chicago, Indiana, resident Antonio J. Lopez.

Authorities withheld the name of the third person killed, a 24-year-old woman, pending notification of her family.

Ledesma was shot in the head. The others suffered multiple gunshot wounds, according to autopsy results released Monday.

Ald. Susan Sadlowski Garza’s 10th Ward office is about three blocks south of the home where the shooting occurred.

“Right now they’re calling it self-defense,” she said, noting that she’d received details about the shooting from the commander of the 4th District police station.

The shooting happened within a block of St. Francis de Sales High School and steps away from 103rd and Ewing, where a bus picks up students who attend Catholic schools in other parts of the city, according to one neighborhood resident.