The government is threatening to take action against the people behind the protest on Tuesday at a forum held by the charter drafters at Thammasat University's Rangsit campus.
Deputy Prime Minister and Defence Minister Prawit Wongsuwon said he believed there must be a hidden agenda behind the protest but he could not blame the student activists who took part.
They were still young and would understand things better when they grow up, he said.
The interim charter says no activities, either to support or protest against the draft constitution, are permitted, Gen Prawit said.
Constitution Drafting Committee (CDC) chairman Meechai Ruchupan was at Tuesday's forum to provide an explanation about the draft charter to the audience who were mainly students.
The protest would be acceptable if the protesting students acted in honesty, said Gen Prawit.
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"However, if it's later proven that others were behind the activity, the National Council for Peace and Order [NCPO] will see what it will do with those people," he said.
He shrugged off criticism the government was depriving the students of the rights to express their thoughts, saying the government has to enforce its powers allowed under the constitution to ensure the CDC can communicate with the public about the drafter before the referendum will be held.
Neither propaganda-style campaigns nor campaigns against the draft charter will be allowed, he said.
Asked if the NCPO would require the students protesting against the draft to attend a military seminar to improve their understanding of democracy, Gen Prawit said the NCPO would find out who exactly was behind the students' activities as the NCPO would rather avoid taking action against students acting honestly.
Pol Col Krisana Pattanacharoen, deputy spokesman of the Royal Thai Police, said police were drawing up a list of names of possible suspects.
Student activist Sirawith "Ja New" Seritiwat, who has several cases associated with his previous activities before the courts, was identified as one of the students attending and disrupting Tuesday's forum, said Pol Col Krisana.
Police were considering if Mr Sirawith had broken any more laws, he said.
CDC spokesman Udom Rathamarit, meanwhile, appeared optimistic about protests against the draft charter, saying he did not think they would turn violent because the CDC does not stand to benefit either way.
He said he viewed the protest as a symbolic gesture that actually was intended for the NCPO.
In another development, the NCPO has summoned a former Pheu Thai MP for Nan to take a "training course" at the 38th Military Circle in Nan province over the red bowl squabble.
The party's acting deputy secretary-general Chavalit Wichayasut said he was disappointed when he learned that former MP Cholnan Srikaew had been summoned to the military unit.
Authorities recently seized nearly 9,000 red plastic bowls from the office of ex-Pheu Thai MP for Nan Sirintorn Ramasut that were provided by former prime minister Thaksin Shinawatra.
Ms Sirintorn was summoned by the military for seven days of "attitude adjustment" that begins on Saturday. Dr Cholnan's seven-day detention begins tomorrow.
The bowls bear a politically tinged Songkran message from Thaksin, who is on the run from a two-year jail term for corruption.
Some of the bowls were also seized from Dr Cholnan's office.
The junta claimed the bowls, intended for use during the Songkran water festival, would cause disunity.
