The scandal is the largest ever to come close to Erdogan, who has led Turkey since 2002 as the head of a conservative Islamic-leaning government.
Judges in Istanbul charged the sons of Interior Minister Muammer Guler, Baris Guler, and of Economy Minister Zafer Caglayan, Kaan Caglayan, with acting as intermediaries in order to give and take bribes, the Hurriyet newspaper reported without elaborating.
The crisis erupted Tuesday when police arrested scores of people in a series of dawn raids that went to the heart of Erdogan's government.
The prime minister has described the corruption probe, which comes ahead of crucial March local polls, as a smear operation targeting his government.
Erdogan has responded by sacking dozens of police officials for cooperating with the probe without permission.
Among those detained were the chief executive of state-owned bank Halkbank, Suleyman Aslan, and the Azerbaijani businessman Reza Zarrab.
Zarrab was charged with forming a ring that bribed officials to disguise illegal gold sales to sanctions-hit Iran via Halkbank, Hurriyet said.
Aslan was charged with taking bribes, the newspaper said without elaborating.
The son of Environment Minister Erdogan Bayraktar was also arrested but 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.
The crisis has rattled the stock market and sent the Turkish lira to an all-time low.
Since the scandal broke out, Erdogan has sacked dozens of officials including the Istanbul police chief in a spectacular purge of the police forces.
Turkish media said another 17 were fired on Friday alone.
Erdogan's critics accuse him of seeking 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.
Kemal Kilicdaroglu, leader of the main opposition Republican People's Party (CHP), called Erdogan a "dictator".
"In this country, everything is controlled by what comes out of a dictator's mouth.... They want to drag the country into the darkness of 19th century," Kilicdaroglu said.
"Turkey needs clean politics and a clean society."
But Deputy Prime Minister Bulent Arinc, speaking at the close of a parliamentary budget debate Friday, said the government was the victim of a conspiracy.
"We don't deserve this. Who else has waged such a determined fight against corruption?" he said to opposition heckling.
Turkey's EU Affairs Minister Egemen Bagis also branded the probe a "disgusting conspiracy".
Erdogan has said he is battling "a state within a state", although neither he nor his allies said who could be behind what Arinc called a "lynch campaign" against them.
Most observers have interpreted the raids as a result of tensions between Erdogan's government and Fethullah Gulen, a Muslim cleric whose followers have been embroiled in a bitter dispute with the AKP after government plans to shut down a network of private schools run by Gulen's Hizmet (Service) movement.
Gulen lives in exile in the United States, but his organization wields considerable influence in several arms of Turkey's state apparatus including the police, secret services and the judiciary.
The graft probe has exposed bitter fault lines in Erdogan's traditional power base and drawn calls for the government's resignation from both his own party and the opposition.
The European Union, which Ankara aspires to join, on Thursday urged Turkish authorities to investigate the allegations in an "impartial manner".
The government's allegation of a plot against it echoes its reaction to mass protests that shook the country in June, when a police crackdown on a peaceful sit-in in Istanbul sparked huge demonstrations against the prime minister and his party.
At least six people died and 8,000 were hurt in three weeks of protests.