"There will not be any presidential guard as we do not need it any more", Binali Yildirim said.
The presidential guard numbers around 2,500 soldiers, but at least 283 were detained after last week's uprising.
Turkish President Recep Tayyip Erdogan addresses people demonstrating against the Parallel State/Gulenist Terrorist Organization's failed military coup attempt in Turkey, via video conferencing at the Turkish Presidency in Ankara, Turkey on July 24, 2016. Turkish officials have blamed a failed coup attempt on Gulen, who denies the accusation. Halis Hanci, who was taken into custody in northern Turkey, entered the country two days before the military coup attempt, the source said. Authorities detained Muslim cleric Fethullah Gulen after he was accused of starting and facilitating the military coup attempt. The state of emergency declared by Erdogan gives his government the ability to declare laws without parliamentary support while suspending civil rights and freedoms arbitrarily as the government decides.
"This is a day to unite, a day to stand up against coups and dictatorial regimes, a day to let the voice of the people be heard", he said at the rally, organised by his secularist opposition CHP but also backed by the ruling Islamist-rooted AK Party and by other opposition groups.
He rejected the European criticism of his iron-fisted response to the coup, charging that "they are biased, they are prejudiced, and they will continue to act in this prejudiced manner towards Turkey".
Turkish officials say they will respect the rule of law during the state of emergency, although some commentators have wondered whether the purges are targeting opponents of Erdogan who had nothing to do with the coup.
In May this year, another nephew of the former imam in self-imposed exile was detained in connection with schools run by the movement, according to a state media report at the time.
The announcement comes as President Recep Tayyip Erdogan decreed that police could hold suspects for up to a month without charge under new state of emergency powers.
Turkish ministers have taken to media, Twitter and conference calls to insist the state of emergency is aimed exclusively at those associated with the coup, that life for ordinary people won't be affected and that economic reforms will continue. "Come here and see how serious this is".
As part of the crackdown, over 1,000 private schools and more than 1,200 associations and foundations believed to be linked to Gulen are set to be closed.
Also, Turkey has freed 1,200 soldiers detained after the failed military coup, Ankara's chief prosecutor Harun Kodalak said on Saturday.
Meanwhile, on Saturday, more than a thousand army soldiers detained in the wake of the July 15 coup were released. Obama denies any United States involvement in Turkey coup bid President Barack Obama on Friday denied any U.S. role in Turkey's failed coup and insisted that an extradition request for a US-based Muslim cleric accused of orchestrating the putsch would have to go through normal channels.