The Turkish government has accused Fethullah Gulen, the spiritual leader of the Hizmet movement, of trying to run a parallel state.
Turkish media said the arrests include senior bureaucrats and police officers.
Fethullah Gulen was once an ally of President Recep Tayyip Erdogan, whose AK party was resoundingly re-elected on November 1.
However, the two fell out, and Fethullah Gulen now lives in self-imposed exile in the US.
A Turkish court issued an arrest warrant for the influential cleric in 2014, accusing him of establishing and running an “armed terrorist group” – a claim the cleric strongly denies.
The state-run Anadolu Agency said those detained in today’s raids were suspected of acting “beyond their legal authority”.
Recep Tayyip Erdogan has decried the work of Fethullah Gulen’s followers as that of “a state within a state”.
He has been seeking to curb the reach the Hizmet movement since 2013.
Last week Turkish police stormed the headquarters of a media group linked to Fethullah Gulen, raising concerns about media freedom days before the country’s election.
The parliamentary election on November 1 followed an earlier, inconclusive poll in June, in which Recep Tayyip Erdogan’s AKP lost its majority in parliament.
The AKP’s victory came amid concerns about rising tensions in Turkey.
Turkey has stepped up operations against ISIS since it was blamed for twin blasts that killed more than 100 people in Ankara last month.
The double bombing, targeting a Kurdish peace rally, was Turkey’s most deadly, and came amid an upsurge of fighting between Turkish forces and Kurdistan Workers’ Party (PKK) rebels.
On November 2, the Turkish military said it had carried out air strikes on PKK militant bases across the border in northern Iraq – the first on PKK targets in Iraq since November 1 election.
In a statement on November 3, the military said that Turkish jets hit PKK shelters, bunkers and weapon storages in six locations, including the Qandil mountains where the rebel leaders are based.
The military has been targeting bases and hideouts of the PKK since July, when renewed fighting between the rebels and Turkish security forces broke out, signaling a breakdown in a two-year ceasefire.
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