A Maryland man went on a deadly rampage over the weekend where he gunned down four people, including his parents, before setting his apartment on fire and killing himself, authorities said. 

Authorities said they "have no idea" what prompted Joshua Green's Sunday killing spree. 

"As to why this occurred, we have no idea yet," Baltimore County Police Col. Andre Davis said at a Monday news conference. "Our homicide detectives are tirelessly investigating a motive, but it appears that the shooter acted alone."

Baltimore County Police Col. Andre Davis, left, and Police Chief Melissa Hyatt are shown at a news conference in Baltimore County on Monday. Investigators have "no idea" why a Maryland man fatally shot his parents at their home and gunned down two other people at a convenience store before setting fire to his apartment and killing himself, a police official said Monday. (Lloyd/The Baltimore Sun via AP)

Investigators said Green, 27, killed his parents -- Douglas Green, 58, and Olivia Green, 62 -- in their Baltimore County home before going to the Royal Farms convenience store just before 7 a.m. 

Once there, Green fatally shot Alpha Smith, 62, who was sitting in her car in the store's parking lot and Silvesta Daye, 43, a customer inside the store. 

A 22-year-old man was also shot but was taken to a hospital in stable condition. After the shooting, Green returned to his home and set it ablaze before fatally shooting himself, police said. 

Authorities discovered the bodies of Green's parents when they went to their home to notify them of their son's death. No suspects were being sought in the case, authorities said. 

Green legally purchased the weapon used in the deadly attacks, police said. 

Baltimore County police investigate a shooting on Sunday at the Royal Farms in Essex, Md. Police say two people have been killed and a third person injured in a shooting at the Maryland convenience store and gas station. (Amy Davis/The Baltimore Sun via AP)

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Police Chief Melissa Hyatt said investigators have spoken to a relative of Green but she didn't elaborate.

"When we are able to definitively have facts and information, we will relay that," the chief said. "We just want to make sure that we are putting out accurate information."

The Associated Press contributed to this report.