Chief opposition whip Sutin Klungsang on Tuesday voiced support for calls for the House to hold a general debate or set up a committee to allow students to work with lawmakers in addressing their concerns.
Mr Sutin said there were several ways the government could keep political tensions stemming from the student rallies from spiralling out of control.
"What we're saying here is that there are channels to address their issues," the Pheu Thai Party MP for Maha Sarakham said.
The students' anti-government protests on campuses across the country were sparked by the disbanding of the Future Forward Party on Feb 21 over the 191.2-million-baht loan it took from former party leader Thanathorn Juangroongruangkit. Some high-school students also followed suit.
Concerns have been raised that these rallies could get out of hand with some government MPs suggesting that the House should allow student representatives to air their grievances within the parliamentary system.
Deputy House speaker Supachai Phosu also voiced agreement with the idea of a special session to address the anti-government protests.
"I totally agree with the proposal. It is better to bring such issues before the House so they can be addressed there," he said.
Energy Minister Sontirat Sontijirawong suggested that there should be a forum where people with different opinions could exchange views and find common ground.
"The government is ready to listen to all sides despite different views. And when we all listen to each other, we should also search for solutions," he said. Prime Minister Prayut Chan-o-cha said on Tuesday it was up to the House to decide if it would convene a special session.
However, Khunying Sudarat Keyuraphan, Pheu Thai's chief strategist, said it was the government's responsibility to listen to the students and not a matter for the House.
In a separate development, activist Srisuwan Janya on Tuesday criticised a Chulalongkorn student activist who tried to fly a black flag at the university's campus during the Feb 24 flash mob.
In a video clip shared online, the female student was stopped by security guards before being able to fly the flag as part of the protest.
Mr Srisuwan said such stunts undermine the students' legitimacy.
Meanwhile, Interior Minister Anupong Paojinda on Tuesday shrugged off the opposition's plan to hold mobile forums nationwide to extend the censure debate across the country, saying they could do it as long as they kept within the law.
He was responding to media reports that the six-party opposition alliance would launch the debate in four regions of the country after two cabinet ministers, he and Deputy Prime Minister Prawit Wongsuwon, escaped a grilling in the House due to "mismanaged" debate time.