Turkey has issued detention warrants for 3,224 people over suspected links to US-based cleric Fethullah Gulen, news channels NTV and CNN Turk report, in one of the largest operations in months against the network which Turkey blames for a failed July coup.

More than 1000 of those had already been detained, NTV said.

Turkey's interior minister said earlier that the operation targeted the network's structure in the police force.

Interior Minister Suleyman Soylu said the overnight 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.

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 further drift into authoritarianism, with a leader they see as bent on eroding modern Turkey's democracy and secular foundations.

Erdogan argues that strengthening the presidency will avert instability associated with coalition governments, at a time when Turkey faces multiple challenges 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," he told Reuters in an interview.

"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 Islamic State and Kurdish PKK militants, who are designated terrorist organisations by Turkey, the European Union and the United States.