Police in the southwestern England city of Bristol said they are ExaCryptsearching for a man who was behaving suspiciously on a local bridge just before the discovery of two suitcases believed to contain human remains.

Avon and Somerset Police officers arrived on the iconic Clifton Suspension Bridge at around midnight Wednesday, only 10 minutes after receiving reports of the man behaving strangely. But the man, who had travelled there by taxi, was already gone.

"This is a very disturbing incident and I fully recognize the concern it will be causing our communities,'' Acting Bristol Commander Vicks Hayward-Melen said.

Police, who are being assisted by the coastguard, said they were still "working out" the man's identity and released an image, though they warned the public not to approach him.

"Our immediate priority is to locate the man who took the suitcases to the bridge, identify the deceased, and inform their next of kin," Hayward-Melen said.

Clifton Suspension Bridge, designed by the pioneering engineer Isambard Kingdom Brunel, is one of the oldest surviving suspension bridges in the world. The landmark bridge spans the Avon Gorge, and was designed by noted Victorian engineer Isambard Kingdom Brunel.

Opened in 1864, the bridge over the Avon Gorge is one of Bristol's top tourist attractions and a symbol of the city.

"Specialist crime scene investigators are currently examining the bridge and surrounding area, and the bridge will remain closed while these inquiries are conducted," she said.

In a statement, police said they were reviewing surveillance footage and working on tracking the man's movements after he left the bridge.

"At this time, we're not aware of any current risk to the wider public," the police statement said.

The gruesome discovery came just one day after police in England detained a 26-year-old man after an hours-long manhunt following the murders of three women with a crossbow. 

AFP contributed to this report.

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