The chief executive of state-owned Halkbank, Suleyman Aslan, and Azerbaijani businessman Reza Zarrab were also charged in connection with the scandal, private NTV and CNN-Turk televisions reported.
Judges in Istanbul charged the sons of Interior Minister Muammer Guler and Economy Minister Zafer Caglayan with acting as intermediaries in order to give and take bribes, the Hurriyet newspaper reported without elaborating.
Zarrab was charged with forming a ring that bribed officials to disguise illegal gold sales to sanctions-hit Iran via Halkbank, Hurriyet said.
It was the first time that such a large scandal has hit those close to Erdogan who has run Turkey since 2002 as the head of a conservative Islamic-leaning government.
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The crisis erupted Tuesday when police arrested scores of people in a series of dawn raids.
Among those detained were Aslan as well as the sons of the interior and economy ministers and that of Environment Minister Erdogan Bayraktar.
But Bayraktar's son was released overnight Friday after hours of questioning by prosecutors and judges. The mayor of Istanbul's conservative Fatih municipality, Mustafa Demir, as well as construction tycoon Ali Agaoglu were also released.
Since the scandal broke, Erdogan has sacked dozens of police officials, including the Istanbul police chief, for cooperating with the investigation without permission.
Turkish media said another 17 were fired on Friday alone, amid a widening purge of the police command.
Erdogan's critics accuse him of desperately trying to protect his cronies, and the appointment of Selami Altinok, a little-known governor with no police career, as Istanbul's new police chief was further seen as an attempt to shut down the investigation.
Altinok raised eyebrows when he landed in Istanbul on Thursday in the premier's private jet.