Mohammed bin Salman said failure to act could embolden Iran and lead to war, which he said would ruin the global economy, following an attack on oil facilities which he blames on Tehran.
Iran said the prince’s remarks would “bring [the Saudis] nothing but shame”.
The prince also said he accepted some responsibility for journalist Jamal Khashoggi’s killing.
But, speaking to CBS News, he denied personally ordering it.
The prince, who is considered the de facto ruler of Saudi Arabia, is suspected of personally targeting Mr Khashoggi, a Saudi journalist critical of the government in Riyadh.
Mr Khashoggi was killed in Saudi Arabia’s consulate in Turkey on 2 October 2018.