The man who killed 6-year-old Coral-Ellen Burrows has pleaded guilty to attempted murder of another man in prison by throwing boiling water on him and stabbing him multiple times.

Stephen Roger Williams, 45, pleaded guilty in the High Court at Wellington this morning to a charge of attempted murder of a 47-year-old fellow inmate.

Williams is serving a life sentence for murder after he beat the Featherston schoolgirl to death while high on methamphetamine in September 2003, then dumped her body by Lake Onoke (Ferry) in Wairarapa.

According to a summary of facts on the most recent offending, on July 31 in Rimutaka Prison, Williams first met the victim the day before when he moved into the cell next to him.

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He offered the victim a cigarette and welcomed him to the unit.

But the next day Corrections officers searched his cell and found tobacco - a contraband item - leading Williams to believe the victim had told Corrections about the cigarette.

Williams sharpened a plastic knife using the blade from a pencil sharpener.

He went to the communal hot water Zip and filled his 1-litre flask with boiling water, then walked into the victim's cell and threw the boiling water over him.

"While the victim was affected by the boiling water, the defendant began striking him in the neck area with the sharpened knife," the summary said.

The victim managed to fight back and escape to the guard hut.

He suffered four stab wounds - one to the back of the head and three to the back of his neck - as well as extensive burns to his neck, chest, upper torso and arms.

In explanation Williams said he planned to kill the victim by stabbing him in the throat.

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Williams is also in preventive detention following the attempted murder of a prisoner at Paremoremo in 2016.

"The prisoner is making it clear that he wants to remain in prison, that's part of the motivation for the offending. This is most unusual and significant, dangerous offending," Crown prosecutor Grant Burston said today.

He said Williams was being moved to a high security prison in Auckland.

Williams will be sentenced on November 1.