It was originally thought that Mark Bridger's appeal bid would be heard by leading judges at the Court of Appeal in London on January 24.
Bridger, a father of six, snatched April near her home in Machynlleth, Mid Wales, on 1st October 2012. Her body has never been found.
Sentencing Bridger in May, Mr Justice Griffith Williams said: "There is no doubt in my mind that you are a paedophile, who has for some time harboured sexual and morbid fantasies about young girls."
Mark Bridger, who was convicted of the murder of five-year-old April Jones, has abandoned his application for permission to appeal against his whole-life tariff, the Judicial Office confirmed today.
The mother of murdered schoolgirl April Jones has said her family continues to be "tortured" by Mark Bridger.
Bridger, who was convicted for the five-year-old's murder, has launched a legal appeal.
Coral Jones said she continues to be "tortured" by Bridger, jailed for life in May.
She claimed that Bridger had tried to claim compensation following an attack by a fellow inmate while at the top security Wakefield Prison, West Yorkshire, earlier this year.
"It's disgusting. He's in prison where he belongs and he should stay there," Mrs Jones told The Sun.
"He's just torturing my family with these legal battles. It's like he's taunting us, like he wants to show he's got the upper hand."
Murderer Mark Bridger, who was jailed for killing five-year-old April Jones, has launched a legal bid, the girl's parents told The Sun.
Parents Coral and Paul Jones said police warned them of an initial hearing at the Court of Appeal next month, which the couple plan to attend.
It is not known whether the appeal is against his conviction or sentence.
Bridger, a father of six, snatched April near her home in Machynlleth, Wales, on October 1 last year.
The five-year-old's body has never been found.
The house where police believe Mark Bridger murdered April Jones may be put up for rent. People living in nearby Machynlleth say they want the house to be demolished. However, authorities say they can't buy it to tear it down, because it's privately owned.
Powys County Council: "As the property is a private dwelling the county council has no remit."
Bridger, 47, abducted the five-year-old as she played with friends near her home in on the Bryn-y-Gog estate in Machynlleth, mid Wales, in October last year. Alexandra Lodge reports.
Mr Justice Coulson, who sentenced Juvinal Ferreira for attacking Mark Bridger over a videolink, said the motive for the attack was no mitigation.
"Convicted murderers cannot appoint themselves as unpaid investigators of another crime, no matter how serious. They plainly cannot do that by themselves committing violent crime to do so."
Leeds Crown Court heard that he used a makeshift knife to slash Bridger from temple to chin, severing an artery.
Robin Frieze, defending, said Ferreira did not attack Bridger to enhance his own status in prison, for reward or because he was incited to do it.
"He was under the impression that if he put the complainant in a state of fear then it was more likely it would achieve closure for the family of his victim," Mr Frieze said.
Bridger abducted and murdered five-year-old April Jones on 1 October last year. Her body has never been found.
April Jones' killer, Mark Bridger, was slashed with a knife fashioned out of a razor at Wakefield Prison.
His attacker Juvinal Ferreira, 24, had five years added to his existing term, at Leeds Crown Court today.
The premeditated attack happened three days after Bridger was allowed to associate with other prisoners.
Ferreira and other life prisoners had talked about attacking Bridger to make him reveal the whereabouts of April's body, police were told.
Jonathan Sharp, prosecuting, said: "He said that Bridger's crime had been discussed, and he claimed people had suggested that if Bridger was attacked, rather than say befriended, Bridger would then be more likely to reveal where April Jones's body was."
Bridger needed more than 30 stitches to the face wound, which required surgery under general anaesthetic. He will be scarred for life.
He also suffered a cut to his arm as he tried to defend himself.
The family of April Jones are expected to attend an inquest into the murdered schoolgirl's death next week.
A hearing will be held in Welshpool on Monday, in preparation for a full inquest in the town at a later date.
Mark Bridger, 47, was given a whole life sentence in May, after being convicted of her abduction and murder.
April was last seen on 1 October 2012, playing outside her home in Machynlleth. Her body has never been found, despite the largest search in British policing history.
Powys coroner Louise Hunt is expected to adjourn the hearing on Monday, after receiving a brief update on the current situation from police.
A spokesman for the coroner's office said a number of April's family would be attended the hearing.
A prisoner has admitted attacking Mark Bridger - the man convicted of the murder of Machynlleth schoolgirl April Jones - inside Wakefield Prison.
Juvinai Ferreira, 22, pleaded guilty to wounding Bridger when he appeared at Leeds Crown Court via video-link this morning.
He will be sentenced on 2 October.
First Minister Carwyn Jones says he will write to the Prime Minister following Mark Bridger's conviction for the murder of April Jones, asking for action to counter the availability of images of child sex abuse on the internet.
Mr Jones was replying to Montgomeryshire AM Russell George. His constituency includes Machynlleth where Mark Bridger abducted April Jones. Hundreds of indecent images were found on the murderer's computer.
Mr George called on the First Minister to support efforts to get internet search companies to adopt a zero-tolerance to such images. He also said that Mark Bridger's conviction and sentencing gave the 'tear in the community fabric' of Machynlleth the chance to heal.