DETROIT — A man suspected of fatally shooting two men and seriously wounding two others had to turn himself in twice before Detroit police would arrest him, authorities said.

Detroit police said the 36-year-old man got into an argument at a party on Saturday, retrieved a gun and opened fire. Four people were shot, and two died. The man turned himself in at a fire station about two hours later, and fire officials called police, but no officers turned up.

Police said in a statement that “due to area patrol units being busy handling high priority runs, no units were dispatched to the location.”

The man eventually went to a police station, where he was arrested.

Police Chief Ralph Godbee said he has ordered an investigation into why no patrol car was sent to the fire station.

Police should have made “every effort to ensure that this person was taken into custody,” he said in the statement sent late Saturday by the department.

Police spokeswoman Sgt. Eren Stephens told the Associated Press on Sunday that the department would examine what police units were doing at the time the suspect tried to surrender, including whether they might have been involved in other aspects of the shooting investigation.

Police did not immediately release the name of the suspect or the victims or provide details on the shooting investigation. They said the men who were shot ranged in age from 19 to 37.

Detroit police have undergone serious personnel cuts under Mayor Dave Bing’s state-supervised effort to close a large budget deficit and avoid a state financial takeover. The city recently imposed a 10 percent pay cut and 12-hour work day for officers.

Sgt. Stephens said the police department wouldn’t immediately comment on the adequacy of its staffing.

Bing spokeswoman Naomi Patton said Sunday that the mayor’s office “had nothing else to say beyond what’s in the police statement.”