A US college lecturer being hunted over the murders of two people has been found dead after apparently shooting himself.

Shannon Lamb had earlier contacted the authorities to tell them he was "not going to jail".

Police in Greenville, Mississippi, were following Lamb as he was driving when the suspect pulled over and jumped out of his car, Lynn Buford, chief of the Delta State University police, said.

One of the victims was killed at the university on Monday.

When police gave chase, they heard one gunshot and then found Lamb. Officers took him to hospital in Greenville where he was pronounced dead of what appeared to be a self-inflicted gunshot wound.

Lamb's death brought to an end a chaotic day that saw terrified students and teachers hiding in classrooms for hours.

The Delta State campus was put on lockdown as armed officers methodically went through buildings, checking in cupboards, behind doors and under tables and desks.

Investigators said Lamb, 45, was a suspect in the killings of 41-year-old Amy Prentiss, who was found dead in the home she shared with him in Gautier, and Ethan Schmidt, 39, a history professor who was shot in his own office on campus in Cleveland 300 miles away.

Lamb received a doctorate in education from Delta State University this spring.

He started working there in 2009 and taught geography and education classes.