An 84-year-old man gunned down his wife and then fatally shot himself Thursday inside the couple’s Long Island home, police said.

Suffolk County Police believe James Paul called 911 after shooting his wife with a handgun and said only “the door’s open” before hanging up, sources told The Post.

“It’s possible he shot himself right after the 911 call,” the police source said.

When cops got to the “very neat, clean” home in Brentwood around 9:25 a.m., they found 79-year-old Rosemary Paul dead of gunshot wounds, police and the source said.

Authorities couldn’t immediately say when she’d been shot.

James, who had also been shot, was taken to Southside Hospital in Bay Shore, where he was pronounced dead.

Both the husband and wife had been sick, the source said.

“Just a very sad situation,” the source added.