"We don't want anything to jeopardise the case that the police are pursuing," Ardern said.
Asked if name suppression laws were out of date with global connectivity, Ardern said: "There's no doubt the environment has changed."
But the Government was not looking at doing any work on name suppression laws, she said.
"At this time, it's not part of our agenda."
The accused's lawyer, Ian Brookie, sought interim name suppression based on fair trial rights, which was opposed by police, the Millane family and the press.
Judge Thomas declined the application for name suppression, but Brookie appealed the decision.
Under the law, an appeal effectively leads to interim name suppression for 20 working days while the appeal is being put together.
Former Attorney-General and current National MP Chris Finlayson and constitutional lawyer Graeme Edgeler said the 20-day rule was too long.
"In general terms, I think these days courts are inclined to want too much paper," Finlayson said.
"You should be able to cut to the chase fairly quickly and present your arguments to the judge within a relatively short space of time ... three or four [days]."
Writing on his blog Legal Beagle, Edgeler said it used to be a matter of judge's discretion before the 20-day rule came into law.
He said the rule "unreasonably affects the public and news media who wish to report on matters of public importance, and which a judge has ruled it is unreasonable to prohibit them from doing so".
"In light of this, 20 working days is excessive."
Edgeler has drafted a bill to reduce the time from 20 to five working days, and offered it to any MP wishing to change the law.
