Mr Ellis had questioned whether the three Justices - Justice Robertson, Justice Judith Potter, and Justice Andrew McGechan - could hear the case.
He argued that they had not been appointed as Justices of the Pitcairn Court of Appeal and could not hear it.
Mr Ellis is also challenging the legality of the search warrant used against his client and said he had only been giving incomplete disclosure from the Attorney-General on the appointments of the Justices.
Crown prosecutor Kieran Raftery also asked for adjournment so all Warren's constitutional arguments could be brought together.
He hinted at the possibility that the case may end up going to "London", a reference to the Privy Council.
But Justice Robertson said the court would look at whether the three justices could hear the case, whether a new oath may need to be taken or whether they should excuse themselves.
"We are conscious that by embarking on this course, it may have to be done again."
Warren has been charged with 20 representative counts of possessing indecent photos of children and five of possessing pornographic images, videos and documents involving children.
Warren was arrested by the New Zealand police officer seconded to the island, which is 5000km northeast of Auckland. The officer made the arrest in 2010 on behalf of the British High Commission.
Two laptops, two hard drives and a CD wallet containing 48 CDs have been confiscated from him.
According to court documents, police examined Warren's computers and found more than 1000 pornographic images and videos of children on them.
While the police searched the home, Warren is alleged to have said he had downloaded pornographic photos and videos to his computers by accident using the file-sharing application Limewire. Limewire has since been shut down.
Warren declined to say anything more to the officer.
In 2004 and 2006, seven of the island's 12 men faced a total of 55 sex crimes, some dating back 40 years. Six were found guilty, with four sentenced to jail terms of up to five years. The crimes included rape, incest and indecent assault against girls from the age of 7.
The then mayor, Steve Christian, was one of those convicted. He was found guilty of five rapes on girls as young as 11. His son Randy was convicted of four rapes and five indecent assaults.
At the time Warren described the criminal proceedings as show trials.
The hearing continues.
