In a television interview, Deputy Crown Prince Mohammed bin Salman also said that his kingdom could withstand a long war in Yemen, where Saudi Arabia fights in support of pro-government forces against Iran-backed rebels.
"How can we get along with a regime which has an extremist ideology... and a profound wish to dominate the Muslim world and spread the Shiite faith?" Prince Mohammed said.
Sunni-majority Saudi Arabia's longstanding accusations of regional interference by Iran have found a more favourable ear in Washington since President Donald Trump took office in January.
The region's leading Shiite and Sunni powers have no diplomatic ties and are at odds over a range of issues, including the wars in Syria and Yemen.
Prince Mohammed said "there are no points of convergence" with Tehran, whose principle aim is to harm his kingdom.
Saudi leaders regularly accuse Iran of stirring regional conflicts by supporting Shiite movements in Syria, Irak and Bahrain as well as in Yemen.
Tehran denies the charges and in turn says Riyadh supports radical Islamist groups.
Prince Mohammed, interviewed on MBC television, said that Iran never acted with sincerity towards Saudi Arabia and that all its attempts at rapprochement were "comedies".
The prince, 31, has risen to become one of the kingdom's most powerful and prominent figures since he was named deputy crown prince two years ago.
-- 'A long war' in Yemen --
He holds the posts of defence minister, heads the main economic policy coordinating body, and is the main proponent of a wide-ranging plan unveiled in April last year to reform the oil-dependent economy.
A Saudi-led coalition intervened in Yemen more than two years ago after Huthi rebels allied with members of the security forces loyal to Yemen's former president, Ali Abdullah Saleh, seized the capital Sanaa and overran other parts of the country.
Both Washington and Riyadh accuse Tehran of arming the Huthis, though analysts say they have seen no evidence of large-scale shipments.
Some analysts say Prince Mohammed must be seen to win in Yemen to protect his leadership future.
The fighting has killed more than 7,700 people over the past two years, according to the United Nations, and the country faces the threat of famine.
Rebels still hold Yemen's capital.
"The Huthis and their allies could be rooted out in several days but the cost would be thousands of dead among our soldiers and losses too high among the Yemeni civilians," the prince said.
He added that "a long war is in our interest", as the coalition has the advantage in arms supply and financing.
The television appearance coincided roughly with the one-year anniversary of the Vision 2030 economic reform plan, which was the focus of the interview.
The Vision plan aims to develop Saudi Arabia's industrial and investment base as well as small and midsize businesses to employ more locals and reduce the reliance on oil revenue.
At the heart of the plan is the sale of less than five percent of state oil company Saudi Aramco on the stock market.
Prince Mohammed confirmed the share sale would take place next year.