MIAMI, Florida (AFP) - Police on Sunday said they still do not know what provoked a rampage by a 42-year-old Cuban-American who shot to death six of his neighbours before being killed by police.

Hialeah police chief Carl Zogby confirmed reports that the suspect, Pedro Vargas, had set fire to US$10,000 (S$12,640) in cash at the start of Friday night's rampage in an apartment building.

"But the reasons for this irrational situation are unknown," Mr Zogby said, who said police were still trying to determine Vargas' motives.

Police believe the incident began when the building's manager, Italo Pisciotti, 79, and his wife Samira, 69, went to his apartment in response to the fire, local press reports said.

He then moved from floor to floor, gunning people down.

Vargas broke into a neighbour's apartment, shooting to death Patricio Simono, 65, Merly Nieves, 51, and their 17-year-old daughter who tried to hide in the bathtub.

At one point, Vargas opened fire from his balcony, killing 33-year-old Carlos Gavilanes as he arrived at his apartment building across the street with his nine-year-old son.

After lengthy negotiations failed to get him to surrender, a police Swat team entered the building early Saturday morning and fatally shot Vargas, who was holding a couple hostage at the time.

Vargas, who lived with his mother, arrived in the United States in 1997 and became a citizen in 2004.

The weapon he used, which has not been identified, was legally purchased, and Vargas had a valid licence, according to police.

Florida, which has the nation's most permissive gun laws, in 2012 became the US state with the greatest number of gun owners.