The authorities are looking to identify people who rallied for monarchy reforms at Thammasat University on Monday, according to Prime Minister Prayut Chan-o-cha.
Speaking after the weekly cabinet meeting, Gen Prayut said those who rallied at the university made comments that potentially violated Section 112 of the Criminal Code, adding the incident must be examined to determine who financed the demonstration and who was behind it.
Students have hit the streets in recent weeks, demanding the resignation of Gen Prayut's cabinet, the dissolution of parliament and the drafting of a new constitution. At the Monday rally, students expanded their demands to include reform of the monarchy, the kingdom's highest institution.
The premier reminded the authorities that opening a probe into such activities is a standard procedure that does not require an order from him.
Gen Prayut also brushed off claims made on social media that police were sent in to arrest students, saying the posts "were hard to verify". However, he said most people would not tolerate the government's failure in taking legal action against law offenders.
He urged protesting students to stick to the facts and be constructive when airing their opinions, adding they should not incite disorder.
The premier also shrugged off the views of 105 academics who lent support to the anti-government students, suggesting the 105 are minority voices in academic circles. He said their stance did not surprise him.
Pol Col Kissana Phathanacharoen, deputy spokesman for the Royal Thai Police, on Thursday expressed concern over the anti-government rallies, which could now be deemed as offensive to the monarchy.
He called on students to respect traditional boundaries for fear of an escalated confrontation with those with opposing views.
Police officers are to be deployed to beef up security during a planned rally on Sunday at the Democracy Monument, Pol Col Kissana said.
Meanwhile, Tipanan Sirichana, deputy spokeswoman of the ruling Palang Pracharath Party, on Thursday called on Pita Limjaroenrat, leader of the Move Forward Party, to clarify his support for the protesting students' 10-point demands, specifically on monarchy reform.
Ms Tipanan said Mr Pita should clarify if his party shares the sentiments. She said executives and members who disagree with Mr Pita should make a written declaration saying so in case Move Forward faces a potential party dissolution over the issue.
Also, Nang Loeng police on Thursday summoned Parit "Penguin" Chiwarak and five other activists to answer questions about a July 20 rally.