"It is impossible that Iran should get undeserved deals," Prince Saud said at a joint news conference with visiting British Foreign Secretary Philip Hammond.
Iran and six world powers are in negotiations to clinch a long-sought deal aimed at putting a nuclear bomb out of reach for the country in exchange for easing sanctions on its economy. Tehran denies wanting nuclear weapons.
Prince Saud called for guarantees that the programme "does not turn into a nuclear weapon that could pose a threat to the region and the world, especially in view of Iran's aggressive politics in the region".
Iran and Saudi Arabia, the foremost Shiite and Sunni Muslim powers in the Middle East, have had troubled relations in recent years after taking different sides in the Syrian civil war.
Tehran has backed Syrian President Bashar al-Assad while Riyadh supported Sunni rebels trying to topple him.