The first reading in the House of Representatives of a civic group-sponsored bill seeking to repeal 35 announcements and orders of the 2014 coup-makers was expected on Wednesday but has been postponed.
However, its backers are optimistic the process will begin next week.
Internet Law Reform Dialogue (iLaw) was told around midday by a member of staff at parliament that its bill would not be included in yesterday's list of draft laws to be debated.
The reason given was that the first reading would have to be deferred to a later time as there were other bills of higher priority.
iLaw said it expects the bill to be tabled for a first reading next Wednesday.
Rangsiman Rome, an MP and deputy secretary-general of the opposition Move Forward Party, also told reporters it was likely deliberation would begin next week.
"To fellow MPs in the coalition, you too have been badly affected by these orders of the now-dissolved National Council for Peace and Order [NCPO]," he said.
"So, if you still remember that, please vote in support of the bill," he added.
He likened the presence of the NCPO's orders as a chain that has been fastened around Thailand, hindering it from moving forward to a more promising future.
Passing the bill would be akin to removing the chain, he said.
According to iLaw, it began drumming up support for the bill in January 2018 and later submitted it to parliament on June 24, 2019, along with signatures of 13,409 supporters.
It said it was informed last Thursday that the bill would enter House deliberation yesterday.