"At this stage we can't find a particular motive, but it does appear to be random in terms of the selection of people who were attacked," he said.
Britain's Foreign Secretary Dominic Raab said he had no information to indicate the incidents were terrorism related but the public should stay "very vigilant".
The first stabbing was in Constitution Hill, police said, and the suspect then moved from north to south, to Livery Street, Irving Street and ending at Hurst Street.
The final location is an area known as the city's Gay Village, where people had been seated at outdoor tables eating and drinking.
A knife was visible to a Reuters witness beside a drain in Edmund Street, near to the second location.
Graham said it was "way too early" to say if the knife was connected to the incident.