A man who took hostages at a bank in rural Louisiana shot his two remaining hostages before being shot and killed by police, authorities said.

The suspect, identified as Fuaed Abdo Ahmed, believed to be in his 20s, had warned he was going to kill the hostages during negotiations with police officers, Louisiana state police superintendent Col Mike Edmonson said.

Ahmed shot the two hostages shortly after state police entered the bank building at midnight on Tuesday. Police shot and killed him, Edmonson said. He said the hostages were shot in the upper body with a handgun and taken from the scene in critical condition. He did not have any other information on their condition but said both showed signs of life when they left the scene.

Edmonson said Ahmed was also armed with a rifle.

Ahmed had initially taken two women and a man captive at about 12.30pm on Tuesday at the Tensas State Bank branch in St Joseph but later released one of the female hostages.

Edmonson said Ahmed was a paranoid schizophrenic and that the situation was not an attempt at bank robbery but a planned attack.

"He was mad at people that he said were mean to him," Edmonson said. "He had voices in his head."