Three women were taken to hospital after being stabbed in Belfast on Monday night.
Two other women were punched, it is believed by the same attacker, who was on a mountain bike and remains at large.
The attacks took place over the course of a one-and-a-half hour period while the victims were walking in south and central Belfast.
Police said a "small sharp knife" is believed to have been used.
All the women were aged between 19 and 22.
One victim was stabbed in the arm, one in the neck and one in the back of the leg.
The two women who were assaulted were punched in the head.
Police said none of their injuries are believed to be life-threatening but that it had been a "hugely traumatic experience" for the victims.
The first stabbing happened in Ormeau Avenue, in the city centre, at about 20:10 BST.
A second was reported at 20:45 BST in Donegall Square West, followed by a woman being punched in the neck as she walked along Dunluce Avenue at about 21:00 BST.
The third stabbing happened in University Road at 21:30 BST.
The other incident - in which a woman was punched in the head - happened on the Dublin Road at about 20:55 BST, but was not reported to police until Tuesday morning.
The male suspect, who was on a bike, was wearing dark clothing, possibly a hooded top and was possibly masked, police said.
Officers have called for anyone with information to contact them.
Ch Supt Simon Walls said police are "taking this investigation incredibly seriously.
"We accept the fear that this type of incident causes, however we wish to say that incidents like this in Belfast and across Northern Ireland are indeed rare," he said.
"You will see in Belfast today, in the city centre and towards the university area an enhanced police footprint that will remain in place throughout the evening."
'Be with a friend or groups'
He urged people: "Just be vigilant, know where you are.
"If you are going out, try to be with a friend or in groups.
"Make sure wherever you're going people know where you're going and what time you're meant to be home.
"Carry your mobile phone and, the really important thing, if anybody feels unsafe or frightened, if they think something's about to happen, please dial police on 999 and we will provide an urgent response."
Ch Supt Walls said the attacker said nothing during the attacks.
He said police did not know if the women were specifically targeted.
South Belfast MP Claire Hanna condemned the attacks, saying she was "horrified" by the news.
"Nobody should feel unsafe on the streets of Belfast and the local community are shocked and upset at this attack," she said.
Ms Hanna said her thoughts were with the victims, adding: "This was undoubtedly a highly-distressing incident."