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Essex Police Chief Constable Jim Barker-McCardle said Pc Ian Dibell had "paid the ultimate price" by placing himself in the line of fire while off-duty.
He said: "He was a highly-regarded and well-liked community police officer."This was highly disturbing but police officers know there is a time to grieve and that is when this investigation is complete."
Speaking at a news conference, police also confirmed that the risk to the public was now over following the discovery of Peter Reeve's body.
Mr Barker-McCardle said a number of lines of inquiry were being pursued as to the motive.
He added: "There must have been some sort of catalyst that prompted the scale of a tragedy of this kind."
He said a handgun had been used in the attack and Mr Reeve, who was "largely unknown to police", did not hold a firearms licence.
Essex Police have confirmed that Peter Reeve was the only suspect wanted in connection with the shooting dead of off-duty police officer Ian Dibell in Clacton-on-Sea on Monday.
The family of Pc Dibell called him a "hero" and said he had paid for his actions "in the most devastating way".
The body found at All Saints Church in Writtle near Chelmsford, Essex, is Peter Reeve, 64, the man suspected of shooting dead off-duty police officer Ian Dibell in Clacton-on-Sea on Monday, police said.
Essex police officers have surrounded Writtle village green in the hunt for Peter Reeve, the man suspected of shooting dead off-duty police officer Ian Dibell in Clacton-on-Sea on Monday.
There are also unconfirmed reports a body has been found at All Saints Church in Writtle.A police news conference is scheduled for 10.30am.
Latest ITV News reports
Police have found the body of a man suspected of killing an off-duty officer in a church graveyard in the village of Writtle in Essex.