Parliament President Chuan Leekpai has urged protesters from the two opposing sides in the political conflict to leave the politicians alone so they can get on with their job.
Parliament reconvenes amid tight security on Tuesday for a two-day session to decide whether to accept seven charter amendment drafts for consideration.
"Don't pressure them into voting one way or another," Mr Chuan said. "Better to just let them vote independently."
Six proposals were submitted separately by the coalition government and opposition camp MPs, then debated extensively by MPs and senators in late September. However, a vote was postponed due to a proposal by a group of senators and government MPs to form a panel to study the drafts.
The seventh draft, proposed by civil group Internet Law Reform Dialogue (iLaw) and initially supported by 100,000 people, has been assured of getting its fair share of debate time after clearing the verification process.
Three of the seven drafts, including iLaw's version, seek changes to Section 256 of the constitution to pave the way for the setting up of a charter drafting assembly.
If all seven bills are accepted, parliament must then pick only one for deliberation, said Mr Chuan.
Pol Maj Gen Piya Tawichai, deputy chief of the Metropolitan Police Bureau (MPB) said three groups were planning separate rallies around parliament on Tuesday and Wednesday, especially on Sam Sen Road.
The first group, led by the Thai Pakdee (Loyal Thais), has obtained police permission to hold a gathering on Tuesday from 9am-2pm.
The second group, "the Civil Politics Group'", will hold a rally from 9am-10pm on Tuesday and Wednesday. The third, the Ratsadon (People's Movement), intends to rally in front of parliament but has not yet sought permission, Pol Maj Gen Piya said.
The MPB will send about 1,350 officers to provide security.
Pol Maj Gen Piya also said that the MBP had asked the Marine Department to ensure security along the Chao Phraya River as a protest group had announced plans for a boat rally on the waterway, too.
Pol Maj Gen Piya said a plan was even in place to evacuate parliament if the protesters laid siege to the building.
He also warned against the protesters' plan to hold a feast, including eating moo kratha (pork hot plate) and grilling shrimps on pavements and nearby roads during the rally as that would violate cleanliness, traffic and public health laws.
Prime Minister Prayut Chan-o-cha said security officers would be responsible for controlling demonstrators, and that he had not given them any special instructions.
The prime minister also dismissed a rumour that he had told a close aide he wanted to resign in the face of mounting pressure.
Pheu Thai Party leader Sompong Amornvivat said it was agreed at a meeting of six opposition parties that they would vote to accept all seven charter amendment bills, including the one proposed by iLaw, during Tuesday's parliamentary session.
Deputy chief government whip and Democrat Party MP Chinnaworn Bunyakiat said the government whips' meeting agreed that coalition parties would vote to accept two bills proposed by the coalition government and opposition parties, calling for for the setting up of a charter drafting assembly.
However, the coalition parties would abstain from voting on four other bills proposed by the opposition camp, Mr Chinnaworn said. These specifically require the Senate to implement national reform and to join MPs in voting for a prime minister.
As for the iLaw-sponsored draft, the government whips would decide whether to accept it after Tuesday's debate on the draft, Mr Chinnaworn said.
Move Forward Party leader Pita Limjaroenrat said his party would vote to accept all seven bills and then propose that the iLaw draft be the main bill in the charter amendment process.