A man in his 30s was being questioned by police on Tuesday after a 15-year-old schoolgirl, who was found stabbed in a lift, became the 16th teenager to die violently in London this year.

Officers found the girl, who has not been named by police, on Monday suffering from multiple stab wounds in the lift of a block of flats near Waterloo Station.

Scotland Yard said detectives were keeping an open mind about a motive for the attack but ruled out it being gang-related.

Police said they had arrested the man in the Lambeth area but gave no further details of the suspect.

Media reports said the suspect, who has not been named, could have been obsessed with his victim and been stalking her.

A police spokesman said on Tuesday he was still in custody and being questioned by detectives.

The girl, who was still in her school uniform, was found by a woman and her eight-year-old daughter suffering at least 10 stab wounds to her chest, neck and back, media reports said.

A post mortem was due to be staged later.

She had lived with her parents and older twin-siblings and had celebrated her birthday at the weekend, newspapers said.

London's ambulance service said on Monday it had dispatched a helicopter and ground ambulance to the scene shortly before 4 p.m. "Sadly, despite extensive efforts to resuscitate the patient, she was pronounced dead at the scene," an ambulance service spokeswoman said.

Knife crime has blighted the capital this year with several killings dominating the headlines. Authorities have since launched a campaign to discourage knife crime in the capital.

Home Secretary Jacqui Smith said the girl's murder was an awful crime.

"I don't despair but it is desperately awful when you see those sort of events," she told Sky News.

"Which is why I think we were right working alongside the police... prosecutors and others, particularly over the course of this year, to up our game on tackling knife crime."

Newly-elected London Mayor Boris Johnson has also made tackling youth violence a top priority.