Scotland Yard officers are urgently trying to trace the single male suspect following the four stabbings in the Edmonton area.
One man has been arrested on suspicion of GBH and inquiries continue to establish if he is the individual behind the attacks.
A 45-year-old woman, who was stabbed in the back, and a 23-year-old man are in a critical condition in hospital.
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Detective Chief Inspector Stuart Smillie, from North Area Command, said: ‘We are doing everything we can to apprehend the suspect behind these cowardly and senseless attacks.
‘We are treating the four stabbing related incidents as potentially linked.
‘The four victims are from different backgrounds and appear to have been selected at random due to them being alone and vulnerable.
‘There is nothing to suggest this incident is terror related.
‘We are working on the hypothesis that the single male suspect is acting alone and mental health issues may be a factor.
‘All of the people he has targeted have been walking alone and he has approached from behind without warning.
‘The motive from the stabbing appears to be solely to inflict harm.
‘Early accounts suggest none of the victims were robbed or engaged in conversation before they were attacked.’
The single male suspect who is described as a black man, approximately 6ft 3ins tall, of skinny build and wearing dark clothing, possibly a hooded top.
The first stabbing took place at 7.02pm on Saturday at Aberdeen Road where the 45-year-old victim suffered a stab wound to her back after being attacked by the man.
She was taken to an east London hospital where she remains in a critical condition.
The second incident took place four hours later at around 12.15am with reports of a male suffering stab injuries in Park Avenue.
The 52-year-old man was taken to an east London hospital for treatment of stab injuries. His condition is not life threatening.
The third incident was at 3.55am with reports of a man stabbed at Seven Sisters Tube station.
The 23-year-old man suffered stab injuries and remains in hospital in a critical condition.
Initial inquiries have established that the man may have been attacked in Silver Street, Edmonton.
The last incident took place at 9.43am in Brettenham Road where officers found a 29-year-old man with a stab injury to the back.
He was taken to hospital for an assessment of his injury, and while his injuries are not life-threatening they are potentially life-changing.
One man was arrested on suspicion of GBH at 10.53am in Fore Street.
Police said inquiries continue to establish if he is behind the incidents, and until that is determined, enhanced police activity will continue in and around the area.
Police tape was up and officers were calling at houses along Aberdeen Road on Sunday afternoon accompanied by a police dog.
Officers in forensic suits could be seen along the stretch of road within the police cordon.
Dervish Husseyin, 60, was at his friend's house on Aberdeen Road when the stabbing took place.
Mr Husseyin said the woman had ‘blood on her back’ but did not seem to realise she had been stabbed.
‘She said she only went out for a walk on her own,’ he said.
Natasha Cameron, 45, lives on Aberdeen Road and was walking home from work at a nearby casino after 10pm.
She said she saw officers on her road who told her there had been a stabbing but she was unaware of the later attacks.
‘I was 'oh my God this is the road I live on',’ she said.
Ms Cameron added: ‘I'm scared now because I always walk here from work home.
‘Now I'm definitely taking the bus.’