DUBAI, United Arab Emirates (AP) — Saudi Arabia's King Salman was shown in state media Sunday in apparent good health and working, just days after the arrest of two senior princes triggered speculation about a possible coup attempt or a sudden deterioration in the king's health.

Two people close to the royal family said Saturday that the two princes were under arrest for not supporting Crown Prince Mohammed bin Salman, who has consolidated control of all major levers of power inside the kingdom with the support of his father, King Salman.

The arrests of the king's younger and beloved brother,...