Avon and Somerset Police received a report of a man acting suspiciously on the landmark on Wednesday night (July 10).
Upon arrival, the man had left the area leaving the suitcase behind and a second suitcase was found nearby shortly after.
An investigation was launched as the suitcases are believed to contain human remains, and Clifton Suspension Bridge was closed yesterday (July 11).
Detectives investigating the case have released an image of a man they want to speak to.
He is described as Black with a beard. He was wearing a black Adidas baseball cap, black jeans, a black jacket, black trainers with thick white soles and had a black backpack.
If anyone sees this man, do not approach him and instead call 999, quoting reference 5224180010 to the call handler.
Clifton Suspension Bridge has reopened today to all vehicles and one footway is open for use by pedestrians as bridge works continue.
The Visitor Centre continues to be closed this morning.
9. Clifton Suspension Bridge reopens as manhunt continues
National World
10. Clifton Suspension Bridge reopens as manhunt continues
National World
11. Clifton Suspension Bridge reopens as manhunt continues
National World