A judge on Phuket is now considering the application.
The request for extra time was lodged with Phuket court on October 27, Phuketwan has learned.
The Royal Thai Navy, which initially launched the criminal defamation and Computer Crimes Act suit against journalists Alan Morison and Chutima Sidasathian and Phuketwan's parent company, Big Island Media, sought an additional 30 days in September in which to consider an appeal.
On October 30, the Royal Thai Navy informed the Phuket Provincial Court by letter that it did not intend to appeal.
But three days earlier, the Phuket Prosecutors' office had asked the court for extra time in which to consider an appeal.
There is no obligation for the Phuket Prosecutor's office to inform the defendants' lawyers of such an application.
The Phuketwan journalists told their legal team today about the application by the Phuket Prosecutor's office.
All charges against the two journalists and Big Island Media were comprehensively dismissed by a Phuket judge on September 1.
Parties in the prosecution have had the regulation 30 days in which to appeal the verdict, plus the extra 30 days granted to the Royal Thai Navy.
A judge is now considering whether to grant the request by the Phuket Prosecutor's office for an additional 30 days in which to consider an appeal.
Coincidentally, a policeman from Phuket's Vichit Police Station visited the offices of Phuketwan on Sunday but found the offices closed.
Corporal Decha Damchoom said later in a telephone call that he had been instructed by Phuket Immigration to check the Big Island Media workplace.
He plans to return on Tuesday.
''The only time we've previously been visited by police was when an officer from Vichit Police Station came to tell us we were being sued for criminal defamation and a count under the Computer Crimes Act,'' Morison, an Australian journalist with 49 years' experience, said today.
The initial criminal defamation and Computer Crimes Act case centred on a 41-word paragraph that Phuketwan reproduced in 2013 directly from a Reuters news agency report, part of a series on the Rohingya boatpeople that later won a prestigious Pulitzer prize.
The police did not prosecute the two Reuters journalists who wrote the paragraph, nor did Reuters help the Phuketwan journalists to defend the news agency's words during the three-day trial in July.
On September 1, a Phuket judge comprehensively dismissed all charges.
Morison and Khun Chutima have won international awards and praise for their uninterrupted coverage of the treatment of the stateless Rohingya from Myanmar (Burma) and other boatpeople over the past eight years.
Morison, who funded Phuketwan from his life savings, says the defamation suit has cost him $60,000 to $100,000 in lost revenue.
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