Sir David Amess: Counter-terror police leading investigation into killing of Tory MP
Chief constable Ben-Julian Harrington said the 69-year-old Southend West MP was "simply dispensing his duties when his life was horrifically cut short".
A 25-year-old man has been arrested on suspicion of murder following the attack at Belfairs Methodist Church in Leigh-on-Sea near Southend at midday on Friday and remains in custody.
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Hide AdMr Harrington said "it will be for investigators to determine whether this is a terrorist incident", adding they will be "keeping an open mind" over the motive.
Tory veteran Sir David had been an MP since 1983 and was married with five children.
Essex police, fire and crime commissioner Roger Hirst urged anyone with information about the killing of Sir David Amess to contact the police.
"This is a shocking and utterly despicable attack against somebody who was an outstanding MP and has worked tirelessly for their community for many, many years," he said in a statement outside Southend police station.
"I know from personal experience the passion with which he stood up for and represented this community. He had a big heart.
"It is vital that we give the police all our support to ensure that they can do their job at this time. For anybody who has information, please do not hesitate to contact the police."
Home Secretary Priti Patel has announced that she has asked all police forces in the UK to review security for MPs.