The DUP has suggested that more footage and "other evidence" exists showing a person dressed up as a Hamas militant during Derry Halloween celebrations.
The party criticised the PSNI for “jumping the gun” after it said a picture shared widely online might be fake.
Chief Superintendent Nigel Goddard said there had been no confirmed sightings of the individual.
“I believe this is a fake image,” he said.
“Whatever the intention of this image was, it serves as a timely reminder that not everything online is as it seems.”
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The DUP’s Foyle MLA Gary Middleton called it “unacceptable” that police had “rushed to rubbish the accuracy of this image”.
“Whilst I recognise that enquiries are still taking place, senior officers jumping the gun in this way will do precious little to assuage concerns about fair and effective policing. There are questions about the police approach to this matter.”
Mr Middleton said he had been made aware of Derry residents in possession of footage who could help the investigation.
“It is crucial that those individuals are contacted and that fresh reports by concerned members of the public are followed up effectively,” he said.
Mr Middleton added: “The glorification of terrorism on our streets and at community celebrations attended by children and young people is perverse and must be stamped out."
