Police in Louisiana are searching for an "armed and dangerous" 21-year-old man accused of killing his parents and three others in two separate but related shootings.

Authorities say Dakota Theriot first shot and killed three people on Saturday - his girlfriend, her brother and her father - in Livingston Parish before taking her father's truck and driving to neighbouring Ascension Parish where he shot and killed his parents.

"We are totally focused on finding him. We're following every lead that we come up with," said Livingston Parish Sheriff Jason Ard during an evening news conference streamed online.

Theriot was being sought on charges of first-degree murder and others. He was believed to be driving a stolen 2004 Dodge Ram pick-up truck, grey and silver in colour.

"I would not approach this vehicle. We feel no doubt that Dakota is going to be armed and dangerous, and we need to bring him to justice really quick," said Ascension Parish Sheriff Bobby Webre.

No red flags

Authorities have identified the victims in Livingston Parish as Billy Ernest, 43; Tanner Ernest, 17; and Summer Ernest, 20. Ard said Summer Ernest and Dakota Theriot were in a relationship and that Theriot had been living with her family for a few weeks.

Summer's mother told police that there had not been any red flags before Saturday's multiple shooting, Ard said.

There were also two young children, ages 7 and 1, in the home at the time of the shooting, he said.

Charlenne Bordelon, who lives near the home where the Ernests were killed, told The Advocate newspaper that two young children from the house ran to her home. They were uninjured and asked for help after the shooting.

Armed and dangerous

Authorities earlier identified the other two victims as Theriot's parents - Keith, 50, and Elizabeth Theriot, 50.

Webre said Dakota had lived with his parents briefly but was asked to leave the residence and not return.

They were shot in their trailer on Saturday morning.

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"The father was gravely injured at the time we found him and has since passed away," Webre said. Before Keith Theriot died, authorities were able to get a "dying declaration from him, and only enough information to let us know that it was his son that committed this act", Webre said.

"We do not have a motive. It is still undetermined," Ard said.

Police said there were indications that Theriot was travelling east and may be in another state by now, and that he is believed to be armed with at least one handgun.

Theriot had some run-ins with law enforcement in other parishes that Webre described as misdemeanor-type incidents that did not include violence.

"Certainly nothing of the magnitude that we've seen today," Webre said.

Webre said there was no reason to think Theriot was now targeting someone else but warned that because he's armed and dangerous: "Anybody he comes into contact with could be a target."