Among those freed from detention pending trial were two of the most senior figures charged over the affair - retired general Cetin Dogan, the former head of Turkey's First Army, and lieutenant-general Engin Alan, a former special forces commander.
The men were detained at the end of February alongside around 70 active and retired officers in a swoop that escalated tensions between Prime Minister Tayyip Erdogan's government, which has roots in political Islam, and the conservative secularist establishment, unnerving financial markets.
The officers stand accused of trying to topple a government they see fostering Islamist ambitions, and their arrests have signalled a new inroad into military power.
Anatolian said that of those freed on Thursday ten were serving military officers, while six of those originally detained in connection with the suspected 2003 "Sledgehammer" plot remained in custody.
The court had agreed with the officers' petition to be released, Anatolian said.
Prosecutors are investigating allegations that the suspects conspired to bomb a historic mosque, shoot down a fighter jet and blame Greece and arrest thousands of people to foment social unrest and destabilise Erdogan's government.
The military denies such a plot, saying Sledgehammer was part of a war-games scenario used at a training seminar.
An officer already charged in connection with membership of a suspected ultra-nationalist organization plotting against the government was also charged on Thursday over Sledgehammer, Anatolian reported.
The armed forces have overthrown three governments in outright coups since 1960 and pressured Turkey's first Islamist-led administration to resign in 1997. The army wields considerable influence in the political sphere, but analysts say another military coup is unlikely in Turkey, a candidate for European Union membership.
