Media companies Stuff and NZME are seeking leave to appeal the decision by the High Court to reject the merger they had proposed.
NZME and Stuff, which until Thursday was called Fairfax NZ, say they will ask the Court of Appeal to let them appeal a High Court decision.
In December, the High Court upheld the Commerce Commission's decision to refuse the merger because of their dominance in key media markets and loss of the diversity of media voices.
Between them the two groups publish most of the country's daily and weekend newspapers, and own a major commercial radio network and two leading news websites.
"After careful review and analysis of the High Court's reasons, the companies continue to believe that the NZCC was wrong in fact and wrong in law to decline clearance or authorisation of the merger," NZME said in a statement to the stock exchange.
The companies said the High Court's full judgement showed the Commission underestimated the monetary benefits to the public of the merger.
They said the court increased the range of potential public benefits to between $133 million to $209m from the Commission's estimate of $44m to $204m.
"However the High Court still found that these benefits were outweighed by the expected loss of plurality in the media. The appeal will focus on the issue of plurality," NZME said.
"Given the potentially significant benefits from the merger, NZME is of the view that appealing the High Court decision is in the best interests of NZME, its shareholders and consumers."
An NZME spokesperson said the company was lodging papers with the court today and hoped to be able to present its case in the first half of the year with a decision in the second half.
She said for the time being it was business as usual for the group.
Last year, a competition lawyer said he believed the merger plan was "probably dead in the water."
Andy Glenie of Anderson Creagh Lai said after the High Court decision that he believed the Commerce Commission and the High Court had got the decisions right, and that the Court of Appeal would probably back them.