Members of the Supreme Council of Senior Islamic clerics were the first to file by Abdullah in a Riyadh palace on Wednesday, shake his hand and pronounce their allegiance to him as Saudi Arabia's sixth king.
The ceremony comes one day after world leaders joined ordinary Saudi citizens in paying respects to King Fahd, who died on Monday.
The House of Saud has depended for legitimacy on the support of clerics from the kingdom's strict Wahhabi version of Islam ever since Abdullah's father, Abdul-Aziz bin Saud, welded the Arabian peninsula tribes into a nation under his name in 1932.
Hundreds of tribal chiefs, religious clerics, government officials and uniformed senior armed forces officers waited in the big hall of the palace for their turn to honour Abdullah. A palace servant swung an incense burner among them in accordance with Saudi tradition.
In the ceremony, known as "bayah", each one shakes Abdullah's hand and pronounces, "I express my allegiance to you. I hear and obey, except in what would disobey God."
It has its roots in the succession after the death of Islam's prophet Muhammad in the 7th century, when the caliphs that followed him received personally the support of the Muslim community.
Security was tight in the Riyadh governor's palace, with armed agents wandering in the hall, wearing traditional white robes and red headdresses, toting automatic weapons and loops of ammunition.
In theory, the ceremony is open to all citizens, but security forces closed off the neighbourhood surrounding the palace, setting up checkpoints, and filtered those who wanted to come in. They checked ID cards, letting in those who were important and turning back others. Two helicopters hovered over the building.
King Fahd was buried in an
unmarked grave on Tuesday
Before the ceremony, Abdullah received Britain's Prince Charles and other Western dignitaries.
Abdullah, dressed in white robes and headdress and cream-coloured cloak, sat chatting with Charles, who expressed his condolences for the death of Fahd and his congratulations for Abdullah's ascension to the throne. Prince Bandar, the former Saudi ambassador to Washington, sat nearby translating.
The Saudi monarch also met Sweden's King Carl XVI Gustaf, the Swiss president and other Western dignitaries, who had been unable to attend funeral ceremonies, which were closed to non-Muslims, a day earlier.
US Vice President Dick Cheney was headed to the kingdom, a close US ally, and was expected to meet Abdullah later on Wednesday.
French President Jacques Chirac and Polish Prime Minister Marek Belka were among the other world figures who came on Tuesday to pay respects.
Representatives of several nations
arrived in Riyadh for the funeral
Fahd, believed to have been 84, was buried in an unmarked grave at the al-Aud public cemetery in Riyadh after brief prayers at the Imam Turki bin Abdullah mosque during which dozens of Arab and Muslim leaders joined members of the Al Saud ruling family.
Saudi Arabia's grand mufti, Shaikh Abdul Aziz Al al-Shaikh, has called on citizens to rally behind King Abdullah and his crown prince, marking the endorsement of the official religious establishment.
Fahd, who carried the title of "custodian of the two holy mosques" in Makka and Madina, Islam's holiest sites, was buried on Tuesday.
Saudis will also show their allegiance to the new 82-year-old king, who has inherited the title of "custodian of the two holy mosques," by visiting ruling family members who serve as governors of provinces in the vast Gulf country.
Across the Arab world, governments have announced periods of mourning for Fahd, whose last years saw his country rocked by a wave of al-Qaida violence.
An Arab summit that had been due to be held in Egypt on Wednesday was postponed.