Saudi Arabia’s deputy crown prince has said there is no space for dialogue with the Iran due to its ambitions “to control the Islamic world”.

The rare and wide-ranging interview, which aired on multiple Saudi TV channels, offered a glimpse into how Mohammed bin Salman al-Saud views the kingdom’s top rival. It also laid bare the breadth of his portfolio and powers.

The 31-year-old prince, who was named in 2015 by his father, King Salman, as an eventual heir to the throne, is Saudi Arabia’s defence minister, overseeing the war in Yemen against a rebel group aligned with Iran. He also oversees economic matters and is behind a bold programme to overhaul the Saudi economy.

Framing the tensions with Iran in sectarian terms, he said it is Tehran’s goal “to control the Islamic world” and to spread its Shia doctrine in preparation for the arrival of a revered imam named Mohammed al-Mahdi. Shia Muslims believe al-Mahdi, the 12th and last Shia imam, who disappeared in the ninth century, will one day reappear to bring justice to the world.

When asked if he sees a possibility for direct dialogue with Iran, the prince replied: “How can I come to an understanding with someone, or a regime, that has an anchoring belief built on an extremist ideology? What are the interests between us? How can I come to an understanding with this?” he said.

Iran and Saudi Arabia’s rivalry has played out in proxy wars across the region. They back opposite sides in the wars in Syria and Yemen and they support political rivals in Lebanon, Bahrain and Iraq. The conflicts have deepened Sunni-Shia enmity between hardliners on both sides.

Ties between Saudi Arabia and Iran have been strained since Iran’s 1979 revolution, with each side competing to be the more powerful force in the Muslim world. Tensions escalated last year, with Saudi Arabia’s execution of a local Shia cleric sparking the ransacking of the Saudi embassy in Iran by protesters. The two countries severed diplomatic and trade ties.

“We know we are a main target of Iran,” Prince Mohammed said. “We are not waiting until there becomes a battle in Saudi Arabia, so we will work so that it becomes a battle for them in Iran and not in Saudi Arabia.”

On Yemen, the prince defended the kingdom’s decision to go to war, which is costing Saudi Arabia tens of millions of dollars a day, according to some estimates. The conflict has worsened an already sweeping humanitarian crisis in Yemen and killed thousands of civilians, mostly as a result of Saudi-led coalition airstrikes.

Experts say the more than two-year-long war has reached a stalemate. Saudi Arabia and its allies have not been able to dislodge the Iranian-allied rebels, known as Houthis, from the capital of Sana’a and other major cities.

When asked about this, Prince Mohammed said the Houthis could be uprooted “in a matter of days”. But, he said, Saudi Arabia has not sent ground troops to retake the capital and other major cities because it would lead to thousands of deaths among Saudi soldiers and Yemeni civilians.

“Time is on our side. Patience is on our side,” he said.