Abdullah had not named a new successor as of Sunday. Under the Saudi system, the title of crown prince of the oil-rich kingdom does not automatically go to the eldest son. A council made up of royal family members appointed by the king chooses a new crown prince from among a group of brothers descended from King Saud.
Al Arabiya said that while the world waited to see who would be the next successor to the 88-year-old Abdullah, tributes to the late crown prince poured into Riyadh.
President Obama said Prince Nayef was a stalwart ally against international terrorism. "Under his leadership, the United States and Saudi Arabia developed a strong and effective partnership in the fight against terrorism, one that has saved countless American and Saudi lives," the president said in a written statement.
French President Francois Hollande said Nayef was "a statesman who left his mark on the development of his country."
Condolences also came from Great Britain, Algeria, Lebanon, Pakistan and the Arab League.