Mohamed bin Salman, making his first public statement since the incident last week, also called on the international community to “take a decisive stand” amid increasing tensions in the region.
Iran has denied any role in the attacks, which came a month after similar blasts crippled two Saudi vessels off the coast of the United Arab Emirates.
The Crown Prince suggested the most recent incident was timed to coincide with Shinzo Abe’s visit to Tehran to mediate between the US and Iran, in an interview with Saudi-owned newspaper Asharq Al Awsat.
“The Iranian regime did not respect the Japanese prime minister’s visit to Tehran and while he was there replied to his efforts by attacking two tankers, one of which was Japanese,” he was quoted as saying. “The kingdom does not want a war in the region but it will not hesitate to deal with any threats to its people, its sovereignty, or its vital interests.”
Saudi Arabia has also accused Iran of arming and training Houthi rebels who seized control of Yemen in late 2015 and have claimed responsibility for recent attacks on a Saudi airport and oil pipeline. The kingdom is leading the military intervention to restore the previous government.
“The problem is in Tehran and not anywhere else,” the prince added. “Iran is always the party that’s escalating in the region, carrying out terrorist attacks and criminal attacks either directly or through its militias. The choice before Iran is clear. Do you want to be a normal state with a constructive role in the international community or do you want to be a rogue state?”
The US military released a video that it claimed proved Iran’s Revolutionary Guards were behind the explosions that damaged the Norwegian-owned Front Altair and the Japanese-owned Kokuka Courageous.
It added to mounting suspicions among intelligence experts that Iran launched the attack as a warning to Washington and others attempting to pressure it over its nuclear programme and support for militant groups throughout the Middle East.
The US has tightened sanctions on Iran since Donald Trump withdrew from the nuclear deal last year and wants to drive down Iranian oil exports, the mainstay of its economy.
Iran has accused the US of waging an “economic war” and threatened to block the Strait of Hormuz through which passes a fifth of the oil consumed globally.
Oil prices have climbed 3.4 per cent since last week's attacks and insurance costs for ships sailing through the Middle East have jumped by at least 10 per cent.
Donald Trump said he was open to holding talks with Iran but declared that any move to close the Strait of Hormuz would not last long.
The US has also accused Iran of firing a surface-to-air missile at a US drone near the Front Altair tanker. The missile did not hit the drone, according to officials.
When asked if more military forces would be sent to the area, acting US defence secretary Patrick Shanahan said they were ”planning various contingencies” but added that the focus was on building an international consensus.
The UK has backed the US position, with foreign secretary Jeremy Hunt saying that responsibility for the attacks “almost certainly lies with Iran”.
However Labour leader Jeremy Corbyn said Britain should not act without “credible evidence”.
Additional reporting by Reuters and Associated Press