Singapore's Home Affairs Minister Teo Chee Hean arrived, as did Venezuelan President Nicolas Maduro, Tanzanian President Jakaya Kikwete, and Libya's internationally- recognised Prime Minister Abdullah al-Thani.
From across the Arab and Muslim worlds, from Europe, Asia, and America, presidents, prime ministers and sheikhs have flown in to express condolences.
It is a recognition of the Islamic kingdom's power as the world's leading oil exporter, a political heavyweight in a region threatened by extremist violence, and as home to Islam's holiest sites.
US President Barack Obama announced he would cut short a visit to India to travel to the kingdom on Tuesday.
Saudi Arabia has long been a key United States ally and last year joined the US-led coalition carrying out air strikes against the Islamic State jihadist group.
Obama "called King Salman bin Abdulaziz from Air Force One today to personally express his sympathies", the White House said on Saturday.
Salman, a half-brother of Abdullah who reigned for almost a decade, declared Sunday a nationwide holiday "to provide comfort and facilitation to all citizens in offering condolences" and allegiance to the new monarch, the official Saudi Press Agency said.
Foreign Minister Mohammad Javad Zarif of Shiite-dominated Iran was among the guests, making a rare visit as Tehran tries to improve relations with its Sunni regional rival.
Both Russian Prime Minister Dmitry Medvedev and Ukraine's President Petro Poroshenko joined the well-wishers, even as pro-Kremlin rebels announced a major new offensive on a strategic government-held Ukrainian port.
Other guests included French President Francois Hollande, Afghan President Ashraf Ghani, Indonesian Vice-President Jusuf Kalla, European royalty and Jordan's King Abdullah II. Prince Charles and Prime Minister David Cameron came from Britain.
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