Also late Saturday, Prime Minister Binali Yilidirim said that the presidential guard is to be completely disbanded.
"There will no longer be a presidential guard, there is no objective, there is no need", the minister told A Haber TV.
Turkey can hold suspects in detention without charge for up to 30 days under its state of emergency imposed in the wake of the failed coup aimed at ousting President Recep Tayyip Erdogan, an official statement said on Saturday.
Halis Hanci, described as Gulen's right-hand man, apparently entered Turkey two days before the abortive coup, a presidency official told reporters.
Human Rights group Amnesty International said it had received credible evidence of detainees being subjected to beatings and torture, including rape, since the coup attempt.
Turkey declared a three-month state of emergency to restore security following the coup attempt, which was foiled by loyalist security forces and pro-government protesters.
And it has disbanded the presidential guard after already detaining almost 300 members suspected of plotting against Erdogan, and detained Muhammet Sait Gulen, a nephew of the cleric who lives in self-imposed exile in Pennsylvania.
Earlier on Saturday, Turkish authorities also detained a nephew of Gulen in connection to the coup attempt, the Anadolu state news agency reported.
Supporters of Turkey's ruling and main opposition parties, usually bitter foes, were set to rally together on Sunday in support of democracy following a failed military coup as President Tayyip Erdogan tightens his grip on the country. "Those responsible for the coup should be tried lawfully, with the understanding of abiding by the rule of law".
President Barack Obama yesterday said the USA would take seriously any "evidence" of wrongdoing by the preacher, whose followers have long had a strong presence in Turkey's police and civil service.
US-based Muslim Cleric Fethullah Gulen, who's nephew has been arrested By the Turkish police. Justice Minister Bekir Bozdag has claimed that "America knows that Fethullah Gulen did this coup".
Despite the high tensions since the coup attempt, the mood at the Istanbul rally was strongly patriotic.
Sunday's mass event, with crowds expected to be boosted by free public transport in the city of 15 million, will seek to soothe divisions after the shock of the July 15 coup and a subsequent government crackdown.
Mr. Brennan, speaking Tuesday evening to an audience at the Intelligence and National Security Alliance, described the setting US officials were in Friday night when the attempted coup was unfolding.
Gulen and Erdogan were allies at the beginning of the Erdogan's government.
The decree authorizes the closure of 1,043 private schools, 1,229 charities and foundations, 19 trade unions, 15 universities and 35 medical institutions over suspected links to the Gulen movement, the Anadolu agency said.
The prime minister elaborated that around 13,000 people were arrested, among who were 1,329 police officers, 8,831 soldiers, 2,100 judges and prosecutors and 689 civilians.