The first victim is identified as 27-year-old Thomas Braxton, who was shot in the head. Police say Caballero then chased 48-year-old Vincent Raleigh into a stairwell and to the third floor, where he shot him in the chest.
Authorities say Caballero then went to apartment 10E, where he lives with his mother, and turned the gun on himself.
Police responding to the carnage heard the shots on the 10th floor, and went upstairs to discover Caballero dead.
The two men who were shot were rushed to nearby hospitals. Officials say Braxton is in very critical condition at Harlem Hospital. Raleigh is in stable condition at St. Luke's Hospital.
Caballero was in his postal uniform when he opened fire, according to witnesses. He was described as a 24-year postal veteran, a model employee.
He was a letter carrier working out of the Sutter Avenue post office in Brooklyn. Postal officials said they did not know what sparked the violence, but that it was not connected to his job.