The normally gridlocked streets of the Saudi capital were quiet after King Salman declared a day of mourning for his predecessor Abdullah, and more foreign leaders made their way to the kingdom.
Venezuelan President Nicolas Maduro was travelling to offer condolences to Salman, who acceded to the throne on Friday after Abdullah's death at the age of about 90.
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 US 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.
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From across the Arab and Muslim worlds, from Europe, Asia, and America, presidents, prime ministers and sheikhs have flown in to pay their respects.
It is a recognition of the conservative 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.
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.
Away from the palace and nearby roadblocks, life continued with almost no indication that a new era had begun, except for billboards expressing condolences for Abdullah's death.
He succumbed to pneumonia.
Even before he became king in 2005, Abdullah had been a force for a decade after King Fahd suffered a stroke.
World leaders have praised Abdullah as a key mediator between Muslims and the West, but activists criticised his rights record and urged Salman to do more to protect free speech and freedoms for women.
"Saudi Arabia is a partner, both economic and political," Hollande said before his arrival in Riyadh with Defence Minister Jean-Yves Le Drian.
Salman, 79, pledged to keep the conservative Muslim kingdom on a steady course and acted to cement his hold on power.
Clearing uncertainty over the transition to the next generation, he named his nephew, Interior Minister Prince Mohammed bin Nayef, 55, as second in-line to the throne behind Muqrin.
Salman also appointed as defence minister one of his own sons, Prince Mohammed.
