One person is in custody in relation to Wednesday night's killing of Constable Duvaughn Brown in Whithorn, Westmoreland.
Senior Superintendent Stephanie Lindsay, head of the Jamaica Constabulary Force's Corporate Communication Unit, says the police are following strong leads.
Constable Brown was a trainee at the National Police College of Jamaica.
The 25-year-old was assigned to the Manchester Division on internship.
Constable Brown was shot about 9:45 in Naggo Town in Whithorn after he left his home to purchase food.
The police are investigating whether a dispute involving some members of Constable Brown's family and other residents may have led to his killing.
Corporal Rohan James, Chairman of the Police Federation, has condemned the killing of Constable Brown. He also used the opportunity to again call attention to the need for improved welfare benefits for rank and file members.
"We will use this opportunity again to implore upon our employer not to wait on the compensation review implementation, but to in fact respond to the security emergency that currently exists and to seek to, as best as possible, alleviate a demoralised force and to provide the resources so that at least every citizen of this country can feel assured that we can respond," he said.
Westmoreland is one of seven police divisions under a State of Public Emergency.
Temper expectations
But SSP Stephanie Lindsay has sought to temper the expectations of residents in Westmoreland who have complained that murders and shootings are still occurring despite the state of emergency.
Residents have told Radio Jamaica News that the presence of the security forces is not being felt.
Speaking on Thursday on the Morning Agenda on Power 106, SSP Lindsay said there will not be a large contingent of police and soldiers descending on the parish.
"We have an SOE, but we're still working with the same numbers. We are still doing all the other policing activities. So, what we have to do now is to use a more tactical approach to how we get to these individuals," she noted.
"So, I just want to reassure the citizens of Westmoreland that the security forces are aware of their concern. We are noting them and we are doing everything to respond to them."
SSP Lindsay also defended the need for states of emergency, agreeing that for the police, the main objective of the anti-crime measure is to remove persons suspected of committing violent crimes from communities. She added that the measure gives police the ability to "conduct extensive investigation without them having the opportunity to carry out a reprisal".
She said, up to Wednesday, four illegal guns had been seized under the states of emergency and several people wanted for serious crimes have been detained.