Iranian Revolutionary Guards drive speedboats in front of an oil tanker at the port of Bandar Abbas Atta Kenare | AFP | Getty Images

On Monday, Trump's national security advisor, John Bolton — who has argued for launching a military strike on Iran's nuclear infrastructure — doubled down on Trump's late-night tweet. “I spoke to the President over the last several days, and President Trump told me that if Iran does anything at all to the negative, they will pay a price like few countries have ever paid before,” he said in a statement on Monday. While war is not imminent, the odds of a military incident occurring in the Persian Gulf is increasing, Cliff Kupchan, chairman at risk consultancy Eurasia Group. "Neither side wants war; Trump seeks to avoid new foreign ventures, Iran knows it would come out on the short end of direct conflict with the U.S. But, when threatened, Iran has a long history of aggressive responses," Kupchan said in a briefing. The rhetoric has been heating up as the first of two U.S.-imposed deadlines for international businesses to cut ties with Iran approaches next month. By November, the United States expects most oil buyers to reduce purchases of Iranian crude to zero or face U.S. sanctions. In May, Trump pulled out of an international nuclear accord with Iran and restored sanctions against the nation, the world's fifth biggest oil producer. This weekend, Iran renewed its threats to shut the Strait of Hormuz, the world's most important seaborne passageway for crude oil shipments. Rouhani mentioned the strait in his speech on Sunday, and Iran's Supreme Leader Ayatollah Ali Khamenei on Saturday endorsed the president's threat to shut the chokepoint if U.S. sanctions disrupt Iran's exports. "Mr Trump! We are the people of dignity and guarantor of security of the waterway of the region throughout the history. Don't play with the lion's tail; you will regret it," Rouhani said. To be sure, the U.S. military and its Gulf allies would be able to reopen the strait in a matter of days, according to Admiral James Stavridis, former Supreme Allied Commander at NATO. However, Iran could repeatedly shut the strait on a temporary basis by mining its waters and using other surreptitious methods, he told CNBC. The U.S. Navy's Fifth Fleet is based in Bahrain and has responsibility for the waterways around the Middle East, including the Strait of Hormuz, the entrance to the Persian Gulf. If Iran were able to lay mines in the Persian Gulf, it would potentially extend the disruption from a couple days to several weeks, McNally estimated. "When you talk about Iran's exports, that's about 2.5 million barrels per day, but if you talk about interrupting the Strait of Hormuz, that's 19 million barrels a day," he told CNBC's "Power Lunch." "About 30 percent of ... seaborne-traded oil goes through that strait. So that's a much bigger problem."

John Kilduff, founding partner at energy hedge fund Again Capital, said Brent crude — the international benchmark for oil prices — is on a path to $90 a barrel because the Trump administration is unlikely to issue many sanctions waivers. Top Cabinet officials have recently said countries could get sanctions relief on a case-by-case basis if they cannot entirely cut off purchases from Iran by November. However, if Iran opts for the "nuclear option" of shutting down the Strait of Hormuz, Brent could pop to several hundred dollars a barrel, in Kilduff's view. "The numbers on a blockage or any kind of upset or military situation in the Strait of Hormuz, that is off to the races. Pick your number — $150, $200 — it goes sky high," he told CNBC's "Squawk Box." "Because we are talking about an abject shortage of oil then in the global market." Brent crude is currently trading just above $73 a barrel. It hit a record high above $147 a barrel in 2008. Rouhani also hinted that Iran could cause problems in other regional sea routes. Those could include Bab el-Mandeb, the strait off the coast of Yemen, where Iranian-aligned rebels are fighting a Saudi-led coalition, said Helima Croft, global head of commodity strategy at RBC Capital Markets.