A man suspected of decapitating a four-year-old girl was beaten by an angry mob as he was detained in Taiwan, with parliament saying it would debate tougher sentences for child-killers following the shocking crime.

The killer grabbed the child from behind as she cycled to a metro station in Taipei with her mother to meet relatives on Monday, and beheaded the child with a kitchen knife, police said.

The suspect pushed away the mother of the girl who had rushed forward to save her daughter, while seven bystanders were also unable to stop the man, who was arrested at the scene, police added. 

The girl has been identified only by the surname Liu, while local media have referred to her by her family nickname "little light bulb".

Police said the suspect, a 33-year-old man surnamed Wang, had been arrested in the past for drug related crimes and had twice sought medical treatment for mental illness after physical altercations with his family.

The case, the second child killing in Taipei in less than a year, has sparked widespread public anger and criticism of calls to abolish the death penalty. 

Taiwan resumed capital punishment in 2010 after a five-year hiatus. Executions are reserved for serious crimes including aggravated murder and kidnapping, but the political elite is divided over whether or not to retain it. 

Following the attack, parliament said it would bring forward to Thursday a review of a bill that would ensure those convicted of killing children under 12 were given the death penalty, or at least a life sentence in the case of severe mental illness. 

"I am deeply saddened by the case ... (the suspect) should be sentenced to death in the case of a stranger killing a child," said lawmaker Wang Yu-min, who proposed the bill.

Children's welfare group the White Rose Social Care Association is planning to hold a mass rally in Taipei on April 9 to push for enforcement of capital punishment in the wake of the crime. 

"This kind of random killing shows that Taiwan cannot afford to abolish the death penalty," said Eva Liang, chairwoman of the association.

The girl's mother, however, urged the public not to discuss the issue of capital punishment to allow the family time to grieve. 

"If you are concerned about us or have sympathy, please respect us ... I don't wish to see such discussions at the time being," she told reporters outside a funeral home, where President Ma Ying-jeou and Premier Chang San-cheng came to pay their respects.

She also asked people not to circulate photos of the girl's body.

  'Stop beating'

Television footage on Monday showed dozens of angry people gathered outside a police station in Taipei where the suspect was being held.

Some attacked the suspect as he was being transferred to the prosecutor's office for questioning, as he pleaded with them to "stop beating".

Others came to lay flowers and toys at the spot where the girl was killed near an elementary school. Her family held a religious ceremony for her there.

Local media said the case may have triggered copycat attacks as two more violent incidents were reported Tuesday. 

In the first case, a knife-wielding man assaulted a metro policeman while he was patrolling a carriage around noon. He was hospitalised for injuries to his head and back, according to the Taipei City police department. 

The policeman immediately pulled the attacker out of the carriage for fear that he could hurt passengers. The man was overpowered by security in the metro station and was arrested at the scene, police said, adding that he claimed he "hates the police."

In New Taipei city, a janitor was injured after being attacked by a man with a small saw. The man tried to flee before he was nabbed near the scene, local police said.