The threatening message was posted on the Facebook page of Sudchai Boonchai, leader of the not well-known Thaksin’s Friends Group.
Deputy army spokesman Winthai Suwaree said Mr Sudchai’s behaviour was extremely inappropriate and was a serious breach of other people’s rights and the family institution.
It was an evil attitude from a person who worships violence, and is very dangerous to society.
“This kind of thing is an attempt to incite disorder and risks committing a serious offence. Such aggressive behaviour poses a serious danger to Thai society. I am confident society will not accept it and call on all parties to consider how he came up with the idea and whether it is proper and fair to Gen Prayuth,” Col Winthai said.
In his Facebook message, Mr Sudchai called on his allies to abduct the twin daughters of Gen Prayuth from the florist shop of Gen Prayuth's sister-in-law in Phitsanulok if Gen Prayuth engineers a coup.
The twins have two armed soldiers as bodyguards at the florist's that also serves as their safe house.
Mr Sudchai, a former leader of the red-shirt Saturday People Against the Coup group, urged supporters to catch the twins either alive or dead.
“Taking them alive as hostages will be very good. But catching them dead is also worth it. Prayuth will know the taste of losing loved ones.
The message has been widely shared on the internet among both pro-and anti-Thaksin supporters.