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

Shannon Lamb had earlier told authorities that he was "not going to jail".

Photo: Gautier Police Department, Reuters

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, told The Associated Press. 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 closets, behind doors and under tables and desks.

University president William LaForge said there would be no classes today but students, faculty and staff were invited to campus to attend a vigil in the evening to honour the professor who was killed.

"We're relieved that this tragedy is over," Mr LaForge said.

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.

Officers in the two cities said they had not uncovered a motive for either killing.

Gautier Police Lieutenant Scott Wilson and another unidentified officer told a press conference they had spoken with Lamb.

They urged extreme caution in dealing with him. In the news conference broadcast on WLOX-TV, the unidentified officer said Lamb told police that he is "not going to jail".

They would not say when or how they spoke to him.

Lamb received a doctorate in education from Delta State University this spring, according to his resume posted on the university's website.

He started working there in 2009 and taught geography and education classes, and volunteered with the home-building charity Habitat for Humanity, according to the resume.

The 3,500-student university in Cleveland, in Mississippi's Delta region near the Arkansas-Mississippi state line, was first put on lockdown mid-morning on Monday amid reports of an active shooter. Everyone on campus was told to take shelter, away from windows.