Saudi royal guards on Friday detained the trio in a move that signals Crown Prince Mohammed bin Salman's tightening grip on power.
The detentions also raised speculation about the health of the 84-year-old king and whether Prince Mohammed's succession to the Arab world's most powerful throne was imminent.
But the official Saudi Press Agency posted photos of the king presiding over the swearing-in ceremony of newly appointed Saudi ambassadors to Ukraine and Uruguay.
A source close to the Saudi leadership told AFP on Saturday the "king is healthy and fine" and the detentions were meant to enforce "discipline" within the royal family.King Salma
The crown prince is "in control" and the purge was carried out "after an accumulation of negative behaviour by the two princes", this source added without elaborating.
Prince Ahmed bin Abdulaziz al-Saud, a brother of King Salman, and the monarch's nephew Prince Mohammed bin Nayef were detained after they were accused of plotting a palace coup aimed at unseating the crown prince, heir to the Saudi throne, sources said.
Prince Nayef's younger brother, Prince Nawaf bin Nayef, was also detained, they added.
The detentions mark the latest crackdown by Prince Mohammed, the king's son who has consolidated his grip on power with the imprisonment of prominent clerics and activists as well as princes and businessmen.
He is already viewed as the de facto ruler, controlling all the major levers of government, from defence to the economy.
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