The government also suspended more than 15,000 state education employees allegedly linked to the "Fethullah Terrorist Organisation" - its name for Gulen's network.
The state of emergency will allow the President and cabinet to bypass parliament in passing new laws and to limit or suspend rights and freedoms as they deem necessary.
Mr Gulen, who has lived in self-imposed exile in the United States since 1999, denies any involvement.
This chaos could have negative effects on Turkish-U.S. relations.
But as of Tuesday, Erdogan's government had yet to restore electricity to the base, which is a vital hub for USA -led air raids against the Islamic State in neighboring Syria and Iraq.
"It's a rampant conspiracy theory among Erdogan opponents that he staged the failed takeover as a pretext for a major crackdown".
That's a question many are asking after the Turkish government ordered the Education Ministry to dismiss more than 15,000 education staff.
A three-month state of emergency has been declared by Turkey's President, following the weekend coup attempt.
In a sign of global concern, a German official said a serious fissure had opened in Turkey and he feared fighting would break out within Germany's large Turkish community.
"A deep split is emerging in Turkish society", Bavarian Interior Minister Joachim Herrmann told the Berliner Zeitung newspaper.
Later, White House spokesman Josh Earnest said that Turkey had submitted materials related to Gulen and the administration was reviewing whether they amounted to a formal extradition request. It does not cover offenses "of a political character", although it does cover "any offense committed or attempted against a head of state", the treaty says. Bagis warned that if the United States ignores the request for Gulen's extradition, it will "run the risk of losing an ally".
"Their bandwidth for the counter-ISIL fight is going to be very, very limited", he said, referring to the Islamic State group.
A spokesman for the Turkish government said the USA should be able to extradite the cleric "on grounds of suspicion" rather than requiring specific facts about the case against him. The crowd chanted "Allahu Akbar" to express their support for the president who has ties to Islamist groups and is seen as a proponent of the Islamisation of Turkey.
"The fact that so many judges have been detained, never mind the workload at the courthouses, will render them inoperable", said Vildan Yirmibesoglu, a human rights lawyer.
"It is ridiculous, irresponsible and false to suggest I had anything to do with the horrific failed coup", he said.
Images of warplanes firing on key government installations, tanks rolling into major cities and news of at least 232 people killed are hardly the backdrop to entice worldwide investors, who are badly needed for the financing of Turkey's sizeable current account deficit, which stood at around 4.5 per cent of the country's annual gross domestic product in 2015.
Tuesday's firings come on top of roughly 9,000 people who have been detained by the government, including security personnel, judges, prosecutors, religious figures and others.
Turkey hasn't executed anyone since 1984, and capital punishment was legally abolished in 2004 as part of Turkey's bid to join the European Union.
Erdogan said Sunday he is receptive to reinstating the country's death penalty in the aftermath of the coup attempt.
Mr Yildirim said Turkey would respect the rule of law and not be driven by revenge in prosecuting suspected coup plotters. "We need to have evidence which we can then make a judgment about".
Speaking to parliament, the chairman of the opposition Nationalist Movement Party, Devlet Bahceli, said his party would back legislation to reintroduce the death penalty if it was put forward by the ruling Justice and Development Party, or AKP. Almost 9,000 people have been detained since the foiled coup on Friday night. Dozens of other generals have been ousted in recent years as Erdogan has repeatedly taken steps against officers he said were plotting to remove him from power.