Cole was a 13-year veteran of the sheriff's department..
"Our deepest condolences go out to the family of fallen Deputy Sheriff Corporal Eugene Cole", LePage said in a tweeted statement.
Gov. Paul LePage offered his support to Maine's law enforcement community as the manhunt continued through the state's central region.
[Update: 1:30 p.m.] - Police have released an updated photo of John Williams, now a suspect in the death of Somerset County Sheriff's Office Cpl. This image was apparently taken from the dash cam of Cole's cruiser. The pictures were captured by the dashboard of Cole's cruiser.
John Williams, 29, of Madison, who is wanted for the death of Cole, remains at large and should be considered armed and unsafe. If people encounter him they should not approach him.
His passenger, a 32-year-old woman from Mercer, Maine, was summonsed for possession of a Class B substance (Percocet), according to police.
"Presently, a manhunt is underway".
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The first line of duty death in ME was Ebenezer Parker, who was killed in 1808 while working for the Cumberland County Sheriff's Department. Eugene Cole and stole his cruiser.
John Williams, 29, reportedly robbed a Cumberland Farms convenience store in Norridgewock, Maine on April 25. The suspect then fled the store in Cole's cruiser.
A search is underway for a man suspected of killing a police officer in central ME and driving away with the officer's squad vehicle early Wednesday - on the same day the suspect was supposed to appear in court in MA, authorities say.
Police said Williams is 5-foot-6, 120 pounds with blue eyes and brown hair in a ponytail.
Williams had a loaded Smith & Wesson handgun with a 16 round magazine in his trunk at the time of his arrest, according to a police report.
A nationwide alert was issued for Williams, Lancaster told reporters. "The suspect should be considered armed and risky".
"We have lost an outstanding deputy today who has served with great distinction for the last 13 years", Somerset County Sheriff Dale Lancaster said in a press conference this morning reported by the Bangor Daily News.