Yingluck Shinawatra, the country's deposed prime minister and Niwattumrong Boonsongpaisan, caretaker premier, were among the 39 prominent figures who reported to the designated military compound in Bangkok on Friday by the 0300 GMT deadline.
The army's intentions for summoning more than 100 people was not clear.
Thailand's army chief, General Prayuth Chan-ocha, seized control of the government on Thursday, two days after he declared martial law, saying the military had to restore order and push through reforms after six months of turmoil.
The military declared a curfew from 10pm until 5am, suspended the constitution and detained some politicians. Rival protest camps were ordered to disperse.
The capital, Bangkok, was calm and activity appeared to be relatively normal early on Friday, although the military has ordered all schools and universities to stay closed.
"There's a little bit more military presence but we're not looking at a situation with tanks rolling onto the streets," Al Jazeera's Scott Heidler, reporting from Bangkok, said.
Regular television schedules were suspended with all stations running the same news programme, featuring content from Channel 5, the army's own channel.
It showed pictures of the areas, now cleared, that had been taken over in and around Bangkok by various political groups since anti-government protests flared up last November.