Saudi Crown Prince Salman "reassured" Saudis during a cabinet meeting on Monday about King Abdullah's health, more than a week after the monarch had surgery to tighten a ligament in his back, state news agency SPA reported.
The king, believed to be in his late 80s, was admitted for surgery on November 16 and an announcement from the Royal Court said he had undergone a successful back operation that took 11 hours.
Saudi stability is of global concern. The key US ally holds more than a fifth of world petroleum reserves and is the birthplace of Islam, where millions of Muslims flock to perform the annual haj pilgrimage.
"His Royal Highness Prince Salman bin Abdulaziz reassured everybody about the health of King Abdullah," SPA said without giving any details or saying when the king might be released from hospital.
The Saudi stock market, which was on a downward trend throughout the day, reversed course and the index closed up 0.4 percent.
Top royals have repeatedly visited King Abdullah at the Riyadh hospital since the operation, SPA said on Saturday, but no photographs of the monarch have been released.
The crown has passed down a line of sons of the kingdom's founder King Abdulaziz Ibn Saud, who died in 1953.
Abdullah - who took power in 2005 - named his brother Prince Salman, 13 years his junior, heir apparent in June after the death of Crown Prince Nayef bin Abdulaziz. Salman deputises for the king while he is away and has chaired both this week and last week's cabinet meetings.