A month before the referendum, 43.6% of voters say they would endorse the draft constitution, according to a poll.
Another 36.8% remain undecided and 13% would abstain while only 6.6% said they would reject it, according to the results of a Bangkok Poll survey released on Saturday.
Some 77.7% of the respondents said they would vote on Aug 7 while 10.4% would not and 11.9% were uncertain.
The survey was conducted between July 5-8 by interviewing people above age 18 nationwide using simple random sampling weighted by Interior Ministry census data. The margin of error was plus or minus 3% at a 95% confidence level.
The results came amid demands for the right to campaign against the new charter by scholars and a group of students, who feel they have not been given the chance to campaign against draft while constitution writers have had numerous chances to explain the strengths of the draft charter.
Seven students were arrested on June 23 for distributing flyers about the weak points of the draft in Samut Prakan province.
Charged with violating the junta's order against illegal assembly and the referendum law, the students refused to apply for bail, saying they had done nothing wrong. The Military Court finally released them on Wednesday and they pledged to continue to with the activity.
Prime Minister Prayut Chan-o-cha said he suspected the students' activities were financed by some people wishing to destabilise the government.