Iran said Foreign Minister Mohammad Javad Zarif would take part in an official ceremony in the Saudi capital on Saturday, without giving further details.
Ex-president Akbar Hashemi Rafsanjani, meanwhile, known for his strong personal relations with the kingdom, called the country a friend and said: "For the deceased I ask for vast blessings from God, for his family and dynasty."
Referring to its new ruler, King Salman, Rafsanjani added: "For your excellency I wish success in consolidating the unity of the Islamic world, prosperity, coexistence and brotherhood of the two nations of Iran and Saudi Arabia under the lofty teachings of Islam."
President Hassan Rouhani also expressed his condolences in a short statement.
Iran and Saudi, seen as the region's foremost Shiite and Sunni Muslim powers, have had troubled relations in recent years after taking different sides in the Syrian civil war.
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Tehran has backed Syrian President Bashar al-Assad while Riyadh supported Sunni rebels trying to topple him.
Since the June 2013 election of Rouhani, seen as a moderate, Iran has engaged in a diplomatic push with Riyadh but relations have soured in recent months over the falling price of oil.
Both countries are members of the OPEC cartel but Iranian officials have expressed frustration at Saudi Arabia for not taking steps to cut supply.
Iran has been among the oil exporting countries worst hit by the fall -- prices have more than halved since June 2014 -- as its current budget is based on sales at $100 (90 euros) per barrel.
Oil prices surged Friday following the death of Abdullah, with investors watching to see if his successor will maintain output in the face of a global supply glut.