Prime Minister Prayut Chan-o-cha insisted he is not against moves by the opposition and the Democrat Party to seek constitutional amendments, despite other coalition parties appearing lukewarm at the idea.
Gen Prayut said on Tuesday he is not opposed to efforts to seek changes. However, he said the charter's opponents should avoid taking to the streets to try and get what they want.
"It's not the government's intention to stop opponents [from protesting]. But we don't want the issue to get out of hand," the premier said.
Deputy Prime Minister Prawit Wongsuwon said on Tuesday the government has other priorities like the flood crisis to attend to.
"Now isn't the time to discuss charter fixes," said Gen Prawit, who is the ruling Palang Pracharath Party's chief strategist.
The coalition parties need to talk the issue over first and ask the people what they think about the push for charter changes since the constitution was passed in a referendum, he said.
The Democrats and the opposition parties have initiated separate motions in parliament to form a committee to study a charter rewrite.
The opposition has complained its motion occupies a lowly spot on parliament's agenda and has asked that it be moved up for prompt consideration. The Democrat motion, however, was not put on the agenda, according to Suthin Khlangsaeng, the chief opposition whip and a Pheu Thai MP.
Deputy Prime Minister and Public Health Minister Anutin Charnvirakul said on Tuesdaythat the Democrats were entitled to their opinion on the charter. However, the Bhumjaithai leader insisted his party did not have to agree with it.
As of now, the party has no plans to push for charter changes, he said.
Prime Minister's Office Minister Tewan Liptapallop, who is also leader of the Chartpattana Party, said the coalition parties have not taken up proposed charter changes for discussion.
Meanwhile, Democrat spokesman Ramet Rattanachaweng said his party has thought the issue through "systematically".
Pheu Thai chief strategist, Khun-ying Sudarat Keyuraphan, said people must be made aware that problems stemming from the constitution have far-reaching ramifications.
She was responding to the latest opinion poll by the National Institute of Development Administration, which said most people do not believe the economy would improve by amending the constitution.
The poll was conducted from Sept 5-6 among 1,260 adults.