The official, declining to be named, said the swoop covers "executives and some staff including columnists", describing Zaman as the "flagship media organisation" of the movement led by Gulen, a US-based preacher.
Turkey govt to work with opposition on new constitution: PM
In March, Zaman and its sister English-language newspaper Today's Zaman were taken over by state-appointed administrators and it has since taken a strongly pro-government line.
The official insisted the warrants were not related to what individual columnists had previously said or written.
But "prominent employees of Zaman are likely to have intimate knowledge of the Gulen network and as such could benefit the investigation", the official explained.
In the attempted coup of July 15, renegade soldiers sought to topple President Recep Tayyip Erdogan but were stopped by crowds of civilians and loyalist security forces. At least 270 people were killed on both sides.
The failed power grab sent shockwaves through Turkish life, and 13,000 people have since been detained.
More than 9,000 of them have been placed in custody ahead of trial over the coup, which the Turkish authorities blame on reclusive Pennsylvania-based cleric Gulen.
Turkey issues warrants for 42 journalists after coup
He strongly denies Ankara's accusations and demanded Tuesday that the United States resists demands for his extradition.
"Turkey's president is blackmailing the United States," he wrote in a New York Times opinion piece.
The swoop on newspaper staff came after authorities on Monday issued another 42 arrest warrants for journalists, including prominent veteran reporters.
London-based rights group Amnesty International said that they represented a "draconian clampdown on freedom of expression".
Among those wanted in the new set of warrants are former Zaman editor-in-chief Abdulhamit Bilici, and former Today's Zaman editor-in-chief and columnist Bulent Kenes, according to the Hurriyet newspaper.
Kenes was previously accused of insulting Erdogan in a series of tweets in late 2015.
Several former Zaman staff are believed to be outside the country following the March takeover of the newspaper.
A major shake-up of the Turkish armed forces is expected to be announced on Thursday when the country's Supreme Military Council meets.
Turkey ruling, opposition parties rally together after coup
With 143 generals and more than 3,000 soldiers arrested on suspicion of links to the coup, there are gaping holes in the command structure which will have to be filled.
Erdogan is also set to visit Russia on August 9 to repair ties harmed by the downing of a Russian warplane by Turkish jets last year, officials said Tuesday, in an apparent sign of Turkey's post-coup diplomatic strategy.
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