Another 2,200 were being sought as authorities targeted what they said was a secret structure within Turkey's police force.
Turkey says a movement loyal to US-based Islamic cleric Fethullah Gulen organised the July 2016 plot to bring down President Recep Tayyip Erdogan.
Earlier this month the president won a referendum on boosting his powers.
As a result of the narrow victory Mr Erdogan can become head of the executive, beefing up the largely ceremonial role of Turkey's president.
"1,009 covert 'imams' in 72 provinces have been taken into custody so far," Interior Minister Suleyman Soylu was reported as saying, calling it an important step for Turkey.
A list of 3,224 people had been compiled by police in an operation across Turkey's 81 provinces, reports said. In Istanbul alone, 390 suspects were being sought.
Erdogan tightens grip - by Mark Lowen, BBC News, Istanbul
It was widely expected that the post-coup purge would accelerate once President Erdogan achieved the victory he wanted in a referendum on expanding his powers.
He feels emboldened and there's no longer a risk of jeopardising potential referendum votes.
No matter that the opposition still contests the referendum results, their claim of widespread fraud backed by a scathing report from election observers. The president says the result is final and that's that.
So on Wednesday the police bore the brunt of the detentions, but other institutions are likely to follow suit.
The governing AKP party was full of Gulen supporters when Mr Erdogan and the cleric were staunch allies.
It hasn't yet been purged and could now be targeted since the president has got his referendum victory. And even if not, it will be dangled over potential opponents like a sword of Damocles: speak out and your Gulen affiliation will be exposed.
Since the coup, in which 249 people died, the government has accused the Gulenist movement of infiltrating the country's institutions including the police, military and judiciary and of running a state within a state.
"We are trying to cleanse members of FETO (the Gulenist movement)" inside the armed forces, inside the judiciary and inside the police," President Erdogan told Reuters shortly before the raids.
Before Wednesday, Turkey said a total of 47,000 people had been detained, including 10,700 police and 7,4000 members of the military. Thousands of people have lost their jobs across Turkey's public institutions, including teachers and civil servants, and opposition media outlets have been closed down.
The Council of Europe's parliamentary assembly angered Turkey on Tuesday by placing the country under review and calling for urgent measures to restore freedom of expression and the press.
President Erdogan, in his interview, accused the EU of "closing its doors on Turkey".
"In Europe, things have become very serious in terms of the extent of Islamophobia," he suggested.
|More than 3,000 people, mainly police, were being targeted in Wednesday's raids. Reuters|
Turkey arrests 1,000 'secret imams' in latest crackdown
Turkey has arrested more than 1,000 alleged Islamists who secretly infiltrated the Turkish police on the orders of a cleric the government blames for last year’s failed coup attempt, authorities said.
The Turkish interior ministry said it had arrested 1,009 members of the Gulen movement, an Islamist group that President Recep Tayyip Erdogan accuses of being behind the coup against him last July.
The movement is led by Fethullah Gulen, a Turkish cleric who is living in exile in the US and was once an ally of Mr Erdogan’s before becoming a bitter rival.
Wednesday’s sweeping arrests were the latest in a broad campaign against alleged Gulenists in Turkey. Around 50,000 people have been arrested since the coup attempt for having links with the movement.
Human rights group says many of those arrested had nothing to do with the coup and only tangential links to Gulenism.
Turkey refers to Gulenists as “secret imams” and says that they had taken up positions inside the police, military and judiciary and were waiting for orders from Mr Gulen to overthrow the government.
Wednesday’s operation was aimed at Gulenists who had infiltrated the police, according to Suleyman Soylu, the interior minister. “1,009 secret imams have been detained so far in 72 provinces, and the operation is ongoing,” he said. “This is an important step for the Republic of Turkey.”
The government said that 8,500 police were taking part in the mass raids across all 81 of Turkey’s provinces.
The raids were the largest in months and come ten days after Mr Erdogan won a disputed referendum that will allow him to change the constitution and vastly increase his own powers.
"We are trying to cleanse members of FETO inside the armed forces, inside the judiciary and inside the police," Mr Erdogan said on Tuesday, referring to the movement by an acronym which means the Gulenist Terrorist Organisation.
Nine months after the coup attempt, which left 249 people dead, it remains unclear how involved Mr Gulen was in the effort to overthrow the government.
Mr Erdogan said Mr Gulen, who now lives in Pennsylvania, had directly ordered his followers in the military to seize power in Turkey. Mr Gulen strongly denies the claim and Western governments have treated the accusation with scepticism.
Turkey has repeatedly asked the US to extradite Mr Gulen so that he can face charges but Washington has repeatedly refused to do so.
Human rights groups have accused Mr Erdogan of using the coup as a pretext to clamp down on political opponents and basic civil rights in Turkey.
“Instead of building on the cross-party unity opposed to the coup to strengthen democracy, Turkey’s government has opted for a ruthless crackdown on critics and opponents,” said Hugh Williamson, Europe and Central Asia director at Human Rights Watch.
Many of those arrested on accusations of Gulenism had only tangential links to the movement, like having a bank account at a bank linked to the Gulenists or sending children to a school where Gulenists taught.