Bhumjaithai Party leader Anutin Charnvirakul insists his party will not abandon the government, despite the protesters' call for Prime Minister Prayut Chan-o-cha to resign.
"[We] come together, [we] go together," he said.
Mr Anutin said neither the cabinet and coalition had yet discussed the possible revocation of Bangkok's state of emergency and he reiterated his party's desire to amend Section 256 of the constitution related to charter amendments.
The party agreed with the establishment of a constitution drafting assembly, he said.
Mr Anutin urged all the protesters to accept that the government was listening to them, as evidenced by the fact it was reconvening the House early next Monday.
Meanwhile, the national Covid-19 task force chaired by the prime minister and the Centre for Covid-19 Situation Administration, on Wednesday approved the extension of the emergency decree until Nov 30.
Mr Anutin, also public health minister, called on all protesters to wear face masks during demonstrations and have alcohol-based hand gels with them, saying that the ministry would send mobile medical teams to provide medical services for them at protest sites.
He also said he had instructed hospitals to be on 24-hour standby to provide medical services for people who might be affected by the ongoing protests.
House Speaker Chuan Leekpai said the extraordinary parliamentary session to debate the current political demonstrations would likely take place next Monday and Tuesday.
Mr Chuan discouraged MPs from using the extraordinary session to verbally attack each other.
Regarding security arrangements, Mr Chuan said there was no need for more security forces from the police or military to be in attendance.
He said it was unlikely that the situation would escalate and said protesters would be allowed to hold activities on the premises, provided they don't use violence or carry weapons.
A House committee is still considering all six drafts of the revised charter but it might not finish in time during the upcoming extraordinary parliamentary session, Mr Chuan said.
The opposition Move Forward Party proposed a few days ago that charter amendments be discussed during next week's extraordinary sessions.
Lawmakers have called for the House, which is in recess, to be recalled early, to move the political conflict from the streets to parliament.
Prime Minister Prayut Chan-o-cha has also said for the first time that he supports a special parliamentary session aimed at easing the escalating political conflict.
Kanchana Silpa-archa, leader of the coalition Chartthaipattana Party, commended the non-voting parliamentary session tentatively scheduled for Monday and Tuesday, saying it would be a good opportunity for lawmakers to discuss all the issues.
Ms Kanchana confirmed that her MPs would take part in the extraordinary sessions, adding that she preferred such a debate to take place inside parliament, not outside.