Representatives of the network filed their written request addressed to NCPO and Army chief Gen Prayuth Chan-ocha at the Army headquarters in Bangkok today.
They urged the NCPO to press charges against Thaksin with a court martial right away.
The representatives said that Pol Lt Col Thaksin supported persons who were insulting the royal institution overseas including Jakrapob Penkair, former prime minister's office minister, who faces an arrest warrant.
Besides, they said Mr Thaksin had initiated the populist policies of the Yingluck Shinawatra government which caused corruption among other national problems.
Mr Thaksin left Thailand in 2008, just before the Supreme Court sentenced him to two-year imprisonment for conflict of interest during his past premiership.
Meanwhile, the NCPO continues summoning people to report to it. Today soldiers brought Kanyaphak Maneejak to report to the NCPO at the Army auditorium in Bangkok's Thewes area.
Also known as DJ Orm, Miss Kanyaphak is a key red shirt leader in Chiang Mai, the home province and political stronghold of the Shinawatra family,
The NCPO's spokesperson team said those who were likely to cause problems would be released just after turning themselves in but those who looked problematic ones would be detained for up to seven days to create understanding.
So far 320 people have been released after reporting to the NCPO.