An army spokesman said a total of 253 people had been summoned. Fifty-three did not report and 76 were in custody.
Conditions for the release appear to include agreeing to avoid political activity and informing the army of travel, a BBC correspondent says.
Coup leaders, who took power last week, received royal endorsement on Monday.
Thailand's former prime minister, Yingluck Shinawatra, has been released but remains under some restrictions.
The army also says it is releasing a group of "red-shirt" protest leaders who support the ousted government. The anti-government protest leader has already been freed.
So far, almost all of the 124 people who the army said they had detained and released have kept a very low profile, says the BBC's Jonah Fisher in Bangkok.
It remains to be seen whether these "red-shirt" leaders - who support the ousted government - do the same, our correspondent adds.
The military seized power in Thailand on 22 May, saying it wanted to return stability after months of unrest.
The move followed six months of political deadlock as protesters rallied against Ms Yingluck's government.
At least 28 people were killed and hundreds injured during the protests.
On Monday a royal command approved the coup. But the military's actions in removing an elected government has drawn widespread international criticism.
Correspondents say there is also a degree of scepticism about the total number of people in custody provided by the military, with reports of more widespread detentions.
Rights groups have expressed alarm over the detentions, as well as the tight restrictions on media.
On Monday, there were reports that internet users were briefly unable to access social media site Facebook. The country's information and technology ministry told the BBC there was a gateway problem.
Experts have said that the coup is unlikely to heal highly polarised political divisions in the country.
The current deadlock dates from 2006, when the military ousted Ms Yingluck's brother, Thaksin Shinawatra, in a coup.
Both have strong support in rural and northern areas, propelling them to successive election wins.
However, many in the middle class and urban elite, who comprise the heart of the anti-government movement that began in November 2013, oppose them bitterly.
Thailand's army says it has now released 124 people, including politicians and activists, who were taken into custody after the coup.