Free Youth and the United Front for Thammasat and Demonstration (UFTD) on Sunday asked their social media followers to switch to communicating with them through Telegram, a messaging application, following rumours the government would ask Facebook to take the groups' pages down.
The groups posted on their Facebook pages that they had learnt the Ministry of Digital Economy and Society had already made the request.
To deal with the problem, Free Youth urged its followers to switch to Telegram and provided instructions on how to set privacy and security settings in the app to conceal their mobile phone numbers.
The UFTD's Facebook page also announced it was moving to a new Facebook account called UFTD V.2 and asked its followers to communicate with it via Telegram as well.
In response to this development, Digital Economy and Society Minister Buddhipongse Punnakanta insisted any decision to try to shut down the protesting groups' pages lay with the police and also requires the acquiescence of Facebook itself.
He said the ministry had not been contacted by police about such an undertaking.
"A shutdown request typically takes considerable time to process -- it requires a court order to proceed," he said.
"The ministry will only consider requesting the takedown of the Free Youth and the UFTD Facebook pages content is posted deemed to be a violation of the emergency decree imposed last week to maintain law and order in the face of growing protests on the streets."
The ministry is obliged to wait for a formal police request, Mr Buddhipongse said.
Phuchaphong Notthaisong, deputy permanent secretary for Digital Economy and Society, said the ministry has no authority to instigate the process of sending a takedown request to Facebook.
However, it may cite the Computer Crime Act to pursue legal action against online offenders.
Under the emergency decree it is National police chief Pol Gen Suwat Jangyodsuk who must first seek a Facebook page be taken down, Mr Phuchaphong said.
