"It's getting more dangerous by the day," he claimed, adding Iran's Ayatollah Ali Khamenei should not be allowed to "develop a nuclear bomb."
"If the Iranians follow through on their threat to start enriching again... and basically take their enrichment program to a nuclear level in terms of weapons-grade production, Israel's in a world of hurt."
The Senate Judiciary Committee chairman added that President Trump should create a "target list" in the case Iran's activities put the U.S. or its allies in danger.
"How do you stop that to make Iran understand you're not going to let that happen?" Graham asked of uranium enrichment.
"He should put the oil refineries on the target list and look at sinking the Iranian Navy if they attack shipping again."
"If I were the president, I would tell the Iranians, if there's an attack on a ship or a pipeline or anything like that, we're going to blow up your oil refinery because they're trying to drive up costs by creating chaos."
Graham clarified he was not calling for any potential "land invasion" but reiterated the United States must be prepared to take action if necessary.
"My red line is - if there's any more disruption of shipping in the [Strait] of Hormuz linked to Iran, take out their Navy, bomb their refineries."
Fox News' Bret Baier contributed to this report.