Butler's lawyers say he is appealing against his conviction and sentence, three Court of Appeal judges heard on Friday.
In June, following a trial at the Old Bailey, Butler was convicted of murdering Ellie and given a minimum 23-year jail term.
Ellie's mother, Jennie Gray, was given a 42-month term after being found guilty of child cruelty, and admitting perverting the course of justice.
Detail of Butler's appeal emerged at a Court of Appeal hearing in London. The three appeal judges - Lord Dyson, Lord Justice McFarlane and Lord Justice Burnett - are considering a different aspect of the Butler case.
They have been asked to decide whether or not a family court judge's behind-closed-doors ruling that relates to Ellie's murder should be made public.
The three-strong panel - headed by Lord Dyson, the Master of the Rolls and the head of civil justice in England and Wales - is scheduled to analyse issues surrounding publication of the ruling at a hearing due to last several hours.
The ruling was made by Mrs Justice Eleanor King following a behind-closed-doors hearing in the Family Division of the High Court in London in the summer of 2014 - after Ellie had died, but before her father had been convicted of murder.
Another family court judge has decided that Mrs Justice King's ruling should not be published in case reporting prejudices any retrial if Butler mounts an appeal.
Mrs Justice Anna Pauffley, who is also based in the Family Division of the High Court, last month rejected an application from several media organisations, who argued that publication of Mrs Justice King's ruling would be in the public interest in the wake of Butler's conviction.
Editors have now challenged Mrs Justice Pauffley's decision. Detail of Butler's appeal was outlined to the three judges by a barrister, Jude Bunting, who is representing editors.
A number of family court judges - including two High Court judges based in the Family Division of the High Court in London - had overseen private hearings about Ellie.
But she was returned to the care of Butler - and her mother - following a ruling by Mrs Justice Hogg in 2012. Mrs Justice King analysed issues in 2014 following Ellie's death.
Ben Butler's police interviewPlay!00:26
Social services bosses at the London Borough of Sutton, who had responsibility for Ellie's welfare, had asked Mrs Justice King to make "findings of fact" to help staff take decisions about the future of a younger sibling.
Mrs Justice King, who is now a Court of Appeal judge, concluded that, on the balance of probabilities, Butler had been "responsible for Ellie's death".
The judge said the little girl had suffered a skull fracture, but her full ruling has not been revealed.
Mrs Justice Pauffley forecast that Mrs Justice King's ruling would make "front page news" if published.
The judge said arguments in favour of Mrs Justice King's ruling being published were "powerful and strong".
But she said publication was likely to generate "very extensive" reporting - and said she had decided that it should remain under wraps if there was "any potential for a retrial".
Several newspapers and broadcasters have applied for Mrs Justice King's judgment to be released.