Police officers in the West Hoe area are stationed on the pavement and in the road.
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There are about five officers in a small area and a police cordon in place. Image caption: The cordons are likely to remain in place for the rest of the day, police said
"Obviously we will keep the public informed as soon as we have more information," they added.
"The cordons are likely to remain in place for the rest of the day and police units will remain in the area."
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Two police officers in yellow are standing on a pavement on the left. There is a police car parked on the right with a police cordon in the distance. Image caption: There will be an increased police presence in the area in the coming days.
BBC reporter Erin Black, who is at the scene, said: "The streets are relatively empty of people and closures are in place from West Hoe Road to Port O Call.
"There are not many people out enjoying what is usually a very beautiful area.
"There were a few people outside Port O Call this morning looking around, wondering what was going on.
"Everything seems to be open, but in a very limited way." There is no atmosphere here. It's like everything has been vacuumed out of the area.
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"It's very grey."
David Badham, general manager of Central Convenience, in Walker Terrace, said the store was within a police security perimeter.
One of his store employees said he heard "screams" and people calling for an ambulance at the time of the incident on Wednesday night.
Mr Badham said when he arrived at work on Thursday morning, officers asked him to keep the doors closed and told him he was not allowed to enter or leave the store.
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