At the start of Monday's ceremony, diplomats from the UN General Assembly's 193 member states stood for a minute in silent tribute to his memory.
UN Secretary-General Ban Ki-moon called Abdullah, who died Jan 23 at the age of 90, "a wise and compassionate leader" and "a champion against global hunger" who sought reconciliation among people of different cultures.
US Ambassador Samantha Power said Abdullah "planted many seeds for Saudi Arabia's future," especially in education with a scholarship program that today has 87,000 Saudis studying in the United States and 33,000 elsewhere in the world.