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.

Daniel Craig will reprise his role as the British spy, with the script penned by Oscar winner, John Logan.
Producers Michael G Wilson and Barbara Broccoli said: "We're really excited to be working once again with Daniel Craig, Sam Mendes and John Logan."
Bond 24 is due for release in the UK on 23 October 2015.
It will have its US release two weeks later, on 6 November.
Mendes, who directed the recently-opened West End musical Charlie and the Chocolate Factory, said he was "very much looking forward to taking up the reins again, and to working with Daniel Craig, Michael G Wilson and Barbara Broccoli for a second time".
He added: "I am very pleased that by giving me the time I need to honour all my theatre commitments, the producers have made it possible for me to direct Bond 24."
Skyfall made $1.1bn (??700m) at the worldwide box office. It was also the highest-grossing film of all time in the UK, earning more than ??94m from ticket sales in 40 days to beat the previous record holder Avatar, which made ??94m in 11 months.
Skyfall won two Oscars - singer Adele's theme song of the same name won best original song and there was an award for sound editing.
It was also named the outstanding British film by Bafta.
It was reported in May that Mendes had resumed talks with producers about directing the next Bond film, having previously ruled himself out due to other commitments.
Mendes is due to follow Charlie and the Chocolate Factory by directing Shakespeare's King Lear at the National Theatre in January 2014.
The last film-maker to lead consecutive Bond movies was former editor John Glen, who directed five films in a row between 1981 to 1989.
Thailand's army says it has now released 124 people, including politicians and activists, who were taken into custody after the coup.
[NEXT_CONCEPT]
Skyfall director Sam Mendes is to direct the 24th James Bond film, due for release in 2015, it has been announced.