The force spoke out following speculation on Twitter about the nature of the incidents.
A police spokeswoman said: "Details are still emerging at this point, but I can say clearly that we do not believe that this is a terrorism related incident."
Two people have today been arrested for attempted murder after two fights broke out in the early hours of this morning.
The first incident reportedly took place in the city centre at about 4am and one person was arrested in relation to this.
Police were then called to a second incident on nearby Cambridge Street at 5.53am in which three people were stabbed and a male hit over the head with a bottle.
A total of five people were injured, with one person is in a serious but stable condition in hospital.
Crime scene investigators in forensic gear appeared to be recovering blood stained white items of clothing from the scene this afternoon.
Detectives said both incidents are believed to be linked and involved the same people.
Four people have been arrested and are in police custody - two on suspicion of attempted murder and two in connection with a public order offence.
A number of streets, including Cambridge Street, Carver Street, Division Street and Barker's Pool, remain cordoned off. There is also no access to Bethell Walk.
Witnesses are urged to call police on 101. Alternatively call Crimestoppers anonymously on 0800 555111.