In a speech broadcast Sunday, Rouhani said the regional rivals could have "good relations" if the Saudis end their "false friendship" with Israel and halt the "inhuman bombardment" of Yemen, where a Saudi-led coalition is battling Iranian-allied rebels known as Houthis.
Saudi Arabia severed diplomatic relations with Iran in January 2016 after Iranian demonstrators attacked Saudi diplomatic missions in response to the Saudi execution of a prominent dissident cleric. Tensions spiked again last month after the Houthis fired a ballistic missile that was intercepted near Riyadh.
Saudi Arabia does not recognize Israel, but the two countries have a shared interest in countering Iran.