Iran's foreign minister arrived in Saudi Arabia on Saturday for a rare visit to the regional rival, bringing condolences after the death of King Abdullah, television pictures showed.

The visit coincided with a statement from Iranian President Hassan Rouhani expressing hope for improved relations with the kingdom.

Saudi officials greeted Iranian Foreign Minister Mohammad Javad Zarif after he landed at a military airport in the capital Riyadh.

Iran and Saudi Arabia, the region's foremost Shiite and Sunni Muslim powers, have had troubled relations after taking different sides in the Syrian civil conflict.

Teheran has backed Syrian President Bashar al-Assad while Riyadh supported Sunni rebels trying to topple him.

Zarif previously declined a Saudi invitation to visit, citing continued negotiations between his country and international powers over Iran's nuclear program.

In August last year, Iran's Deputy Foreign Minister Hossein Amir-Abdollahian held talks with Saudi Foreign Minister Prince Saud al-Faisal in the Red Sea city of Jeddah.

That was the first high-level Iranian visit to Saudi Arabia since Rouhani became Iranian president a year earlier.

They discussed the fight against Islamic State jihadists, whom both nations oppose.

Rouhani has stated his wish to improve relations with Saudi Arabia.

On Saturday, he issued a statement congratulating Saudi Arabia's new King Salman on his accession after Abdullah's death on Friday.

With religious and historic bonds between the two nations, Rouhani said he hoped relations can be improved "more than ever."

"I pray to God for your health and success and prosperity for the nation of Saudi Arabia," he said.

Since the 2013 election of Rouhani, Iran has engaged in a diplomatic push with Riyadh, although relations have soured in recent months over the falling global price of oil.