Oregon State Police said they've received 58 tips after a statewide alert was issued for DiMaggio. None of the sightings has been confirmed.
The Washington State Patrol said several people reported seeing DiMaggio's car.
DiMaggio is believed to be on the run with Hannah Anderson, 16, and possibly her 8-year-old brother Ethan. He went missing Monday night. Anderson's mother was found dead at DiMaggio's burning home. A dead child nearby may be the 8-year-old Ethan, but the body has not been positively identified.
Authorities believe DiMaggio may be driving his blue 2013 Nissan Versa sedan with California license 6WCU986.
The search has been extended to Oregon, Washington and Nevada, as well as Canada and Mexico. The FBI is assisting in the manhunt.
Washington State Patrol Sgt. Jason Hicks says people up and down the Interstate 5 corridor have reported seeing the blue Nissan Versa being sought by authorities. Some reports came in from the Vancouver, Wash., area; some from the Tacoma area; and at least one near Bremerton.
The San Diego County Sheriff's Department said Thursday that a search of DiMaggio's home, east of San Diego, suggests he might have homemade explosives with him.
Authorities are worried he may have booby-trapped his car and warned anyone who may have seen it not to approach the vehicle.
DiMaggio is about 5 feet 9 inches tall, weighing 150 pounds, with brown hair and brown eyes. He has been described as a well-traveled outdoorsman. He is a former friend of Hannah's father, Brett Anderson.
At a Tuesday news conference, Brett Anderson addressed his daughter: "Hannah, we all love you very much. If you have a chance, you take it. You run. You'll be found."
Hannah is about 5-foot-7 and 115 pounds, with blond hair, blue eyes, a navel ring, a nose stud and pierced ears. Ethan was described as about 4 feet 11 inches and 65 pounds, with sandy blond hair.
The case led to the first-ever use of the cellphone Amber Alert system Monday night, which startled many people.
Anyone with information on the possible whereabouts of the suspect or the missing children was asked to immediately call the San Diego County Sheriff's Department at (858) 565-5200.
The Associated Press and City News Service contributed to this report.