Turkish authorities say they have arrested more than a thousand "secret imams" who had infiltrated police forces on behalf of a United States-based cleric accused by President Recep Tayyip Erdogan of trying to topple him last July.

The nationwide sweep was one of the largest operations in months against suspected supporters of the cleric, Fethullah Gulen, a former ally of Erdogan. Gulen denies any part in the coup led by military officers.

Interior Minister Suleyman Soylu said the crackdown targeted a Gulen network "that infiltrated our police force, called secret imams.

"One thousand and nine secret imams have been detained so far in 72 provinces, and the operation is ongoing," he told reporters in Ankara.

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A further 9103 personnel from Turkey's police force were suspended, police headquarters in Ankara said in a statement on its website, citing alleged links with Gulen's network.

In the aftermath of the failed July coup, authorities arrested 40,000 people and sacked or suspended 120,000 from a wide range of professions including soldiers, police, teachers and public servants, over alleged links with terrorist groups.

The latest detentions came 10 days after voters narrowly backed plans to expand Erdogan's already wide powers in a referendum which opposition parties and European election observers said was marred by irregularities.

The referendum bitterly divided Turkey. Erdogan's critics fear a further drift into authoritarianism, with a leader they see as bent on eroding modern Turkey's democracy and secular foundations.

Erdogan argues strengthening the presidency will avert instability associated with coalition governments, at a time when Turkey faces problems including security threats from Islamist and Kurdish militants.

"In Turkey, there was an attempted coup with a goal of toppling the Government and destroying the state. We are trying to cleanse members of Feto inside the armed forces, inside the judiciary and inside the police," he said, using an acronym for the label, Gulenist Terrorist Organisation, which the Government has given to Gulen's supporters.

The President compared the struggle against Gulen with the state's battle against Isis (Islamic State) and Kurdish PKK militants, who are designated terrorist organisations by Turkey, the European Union and the US.

"We are going to keep up the fight in terms of democracy, fundamental rights and liberties, but at the same time we are going to keep up the fight against PKK, Feto and other terrorist organisations such as Daesh [Isis]," he said. "We will continue down this path in a very committed fashion."

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Mass detentions immediately after the attempted coup were supported by many Turks, who agreed with Erdogan when he blamed Gulen for orchestrating the putsch which killed 240 people, mostly civilians. But criticism mounted as the arrests widened.

Many relatives of those detained or sacked since July say they have nothing to do with the armed attempt to overthrow the Government, and are victims of a purge designed to solidify Erdogan's control.