Iran's President Hassan Rouhani called Monday on Saudi Arabia to end what he called the kingdom's "intrusions" in the Middle East in order to allow closer ties between the two regional rivals.

"If Saudi Arabia's vision on the big regional questions confronts reality and it stops its intrusions, we can solve many problems, especially in our relations," Rouhani told a gathering of Iranian ambassadors in Tehran.

Shiite Iran and Sunni Saudi Arabia, the Gulf region's powerhouses, have long had an uneasy relationship and are backing opposing sides in conflicts in Syria and Yemen.

Tehran is strongly opposed to air strikes on Shiite Huthi rebels in Yemen by a Saudi-led coalition, while Riyadh accuses Iran of seeking to destabilise countries with large Shiite populations such as Lebanon and Bahrain.

Iran's deputy foreign minister, Hossein Amir Abdollahian, on Sunday chided Saudi Foreign Minister Adel al-Jubeir, warning him "not to test the limits of the Islamic republic's patience". 

"Instead of blaming others, Saudi Arabia's minister of foreign affairs would do better to end his visible and hidden support for terrorists in Yemen, Iraq and Syria," Abdollahian said. 

Iran joined talks with world powers on Syria for the first time last week when officials from 17 countries, including Saudi Arabia, and the UN and EU met in Vienna in a bid to narrow differences on how to end Syria's civil war.