Turkey widened its massive post-coup purge to the state education sector on Tuesday after vowing to root out supporters of an exiled cleric it accuses of orchestrating the attempted power grab.

Global alarm is mounting over the retaliatory action of the authorities since Friday's attempted putsch, which has seen a massive crackdown in the military, police and judiciary and thousands detained.

Prime Minister Binali Yildirim said Turkey had sent dossiers to the United States to back up its demand for the extradition of Islamic preacher Fethullah Gulen, President Recep Tayyip Erdogan's sworn enemy who lives in exile in Pennsylvania.

"We will pull them (Gulen supporters) out by the roots like a razor blade," he said.

In the latest action by the authorities, the education ministry said more than 15,000 state education employees had been suspended.

Already, around 9,000 people including police and government officials have been sacked and 7,500 people detained including top generals accused of masterminding the plot.

Nevertheless, Yildirim warned Turks against exacting revenge on backers of the attempted government overthrow, after disturbing pictures emerged of rough treatment meted out to suspects.

"Nobody can have a feeling of revenge. This is unacceptable in a state governed by rule of law," Yildirim said.

- 'Nonsensical' claims -

Ankara says the reclusive Gulen, who wields enormous influence in Turkey through supporters in various apparatus as well as a private school network school, hatched the plot to end Erdogan's 13 years in power.

Gulen, 75, has rejected the allegations, saying Erdogan himself may have staged the putsch, an idea dismissed by the presidency Tuesday as "nonsensical".

Turkey's Western allies have urged Ankara to abide by the rule of law amid fears about a worsening state of democracy and human rights.

Erdogan's suggestion the death penalty could be reinstated has also sent shudders through Europe, with the EU warning such a move would be the nail in the coffin of Turkey's already embattled bid to join the bloc.

An Ankara court on Monday charged and put in pre-trial detention 26 former generals over the putsch, including former air force chief General Akin Ozturk, painted by some Turkish media as the mastermind.

But Ozturk denied he was the coup ringleader.

"I am not the person who planned or led the coup. Who planned it and directed it, I do not know," state-run news agency Anadolu quoted him as saying.

Anadolu published images of a haggard-looking Ozturk, one ear heavily bandaged, and other suspects at the courthouse, their hands tied behind their backs.

- Revenge 'unacceptable' -

The coup bid was the most serious threat to Erdogan since he took power first as prime minister in 2003, and saw rebel troops close down bridges in Istanbul, parliament bombed from the sky and protesters shot in the streets.

It has raised deep concerns about the stability of the strategic NATO partner, which has a key base used in the US-led fight against the Islamic State group and which houses a large nuclear weapons stockpile.

A total of 208 people were killed, including 145 civilians, 60 police and three soldiers, along with 104 coup plotters, the government and army says.

The military has often had strained relations with Erdogan's Islamo-conservative government as the traditional guardians of Turkey's secular system and has carried out coups in the past.

But it said the vast majority of its forces had nothing to do with Friday's plot.

It said the "traitors" would be punished severely for the "humiliation and disgrace" of the Turkish republic.

UN rights chief Rights Zeid Ra'ad Al Hussein urged a fair trial for the suspects and voiced "serious alarm" over the mass suspension of judges.

- 'Betrayal of the nation' -

Turkey has blamed Friday's events on what it calls Gulen's "Fetullahci Terror Organisation" (FETO) and piled the pressure on Washington to extradite him.

The reclusive cleric said in an interview at his Pennsylvania compound that he had no concerns about the extradition request.

"The rule of law reigns supreme here. I don't believe this government will pay attention to anything that is not legally sound."

He called the putsch attempt "treason, a betrayal of the Turkish nation."

Erdogan told CNN in his first media interview since the coup bid that he would approve any decision by parliament to reintroduce capital punishment which was abolished in 2004.

But the EU -- which Turkey has for years tried to join in a stalled accession process -- warned of the consequences of such a move.

"No country can become an EU state if it introduces the death penalty," EU foreign affairs chief Federica Mogherini said.

Erdogan has remained in Istanbul since he flew back on Saturday from the holiday resort of Marmaris where he was staying when the coup struck.

The president, who critics have long accused of becoming increasingly autocratic, has spoken to supporters every night, urging them to maintain a "vigil" for democracy.

He told CNN his life had been in grave danger. "If I stayed (in Marmaris) 10, 15 minutes more, I would either have been killed or kidnapped and taken away by them."