"The judicial process on this will continue,” Bozdag said, Al Jazeera reported.
The government quickly began a purge of soldiers and judiciary officials allegedly connected to the plot after it became clear the attempt had failed on Saturday.
By Saturday evening, 2,839 military personnel had been detained, with the number of arrests expected to rise, according to Turkish Prime Minister Binali Yildirim.
The top judicial body, the HSYK, dismissed 2,745 judges on Saturday.
Additionally, a senior Turkish official told Al Jazeera that at least two judges from the constitutional court and 10 judges from the HSYK had been detained.
Speaking on condition of anonymity, the official said that the judges were detained based on "financial transactions and communications between the individuals in question and the putschists", but added that detention did not necessarily mean conviction.
Another senior official, also speaking anonymously, told Al Jazeera that a top army general was also being held over his alleged involvement.
"General Erdal Ozturk, commander of the Third Army, has been detained," he said.
"Our sense is that the would-be junta had made preparations for some time. They had determined which military officers would take over as governors, heads of government agencies ... but they were forced to rush due to the upcoming Supreme Military Council meeting," he said.
The official described Ozturk as "one of the masterminds" behind the plan.
The coup attempt began at around 19:30 GMT on Friday with the partial closure by troops of two major bridges over the Bosphorus in Istanbul as tanks moved into the streets and fighter jets were seen in the skies.