PM Binali Yildirim told A Haber TV channel that there was “no need” for the regiment.
Earlier, Turkey detained Muhammet Sait Gulen – a nephew of US-based cleric Fethullah Gulen who, it says, was behind the uprising.
Fethullah Gulen strongly denies the claim.
A key aide of Fethullah Gulen has also been arrested, a presidency official said.
President Recep Tayyip Erdogan launched a widespread crackdown following the attempted coup, arresting thousands of service personnel and sacking or suspending thousands of government officials, school teachers and university heads.
A state of emergency was declared on July 21, allowing the president and cabinet to bypass parliament when drafting new laws and to restrict or suspend rights and freedoms.
PM Binali Yildirim told the A Haber TV channel: “There will no longer be a presidential guard, there is no purpose, there is no need.”
The presidential guard numbers up to 2,500 soldiers but at least 283 were detained after the uprising.
Fethullah Gulen, a former ally of Recep Tayyip Erdogan, has called on the US government to block Turkey’s attempts to extradite him.
Muhammet Sait Gulen was detained in the north-eastern city of Erzurum to be taken to the capital Ankara for questioning, the Anadolu news agency says.
A presidential official quoted by Reuters said Halis Hanci, described as Fethullah Gulen’s right-hand man, had been “captured”.
According to the official, Halis Hanci had apparently entered Turkey two days before the coup attempt.
On July 23, Recep Erdogan extended the period in which suspects can be detained without charge to 30 days.
A statement carried by state media also ordered the closure of more than 1,000 private schools and more than 1,200 associations.
Also on July 23, Ankara’s chief prosecutor Harun Kodalak was reported by Turkish media as saying that 1,200 soldiers detained in the wake of the coup had been released.
Those freed were said to be low-ranking soldiers. Thousands of other service personnel, including more than 100 generals and admirals, remain in detention.
Recep Erdogan’s tough measures have been criticized by human rights groups, as well as by France, Germany and senior EU officials.
He told France 24 television on July 23 the EU was “biased and prejudiced” against Turkey.
Amnesty International has said Recep Tayyip Erdogan is going “well beyond what might be considered a legitimate response to the coup attempt”.
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