The vessels exited the Strait of Hormuz on Monday, hours before a U.S. naval blockade took effect.

Hours before a U.S. naval blockade of ships from Iranian ports took effect on Monday, two Iranian-linked ships exited the Persian Gulf via the Strait of Hormuz, according to Kpler, a global ship-tracking firm.

The crossings highlighted that although the number of vessels passing through the strait has fallen sharply, ships linked to Iran have continued to navigate the waterway at rates close to those before the first U.S. and Israeli strikes in late February, according to Kpler. Transits in the four weeks to Sunday averaged 2.2 million barrels of oil per day, compared with an average of two million per day in the four weeks to Feb. 28.

One of the ships, the Panama-flagged tanker Auroura, was believed to be carrying a cargo of Iranian naphtha, a type of petroleum product, which Kepler noted was under sanctions and had previously carried Iranian cargoes. The second tanker, the New Future, loaded gas oil at the Hamriyah port in the United Arab Emirates and carried a Marshall Islands flag. The New Future’s previous three trades were with Iran.

There was “still a trickle of trade making its way through” on Monday before the blockade came into effect, said Alexis Ellender, an analyst at Kpler. But major shipping companies not linked to Iran had an “incredibly low” risk appetite for crossing the strait, he said.

The average number of vessels crossing the Strait of Hormuz before the war was more than 120 per day. Just 28 vessels have crossed in the last two days, including 14 on Sunday, mainly ships with links to Iran.

President Trump said Monday that the U.S. Navy would attack any Iranian ships that tried to cross the Strait of Hormuz. “Warning: If any of these ships come anywhere close to our BLOCKADE, they will be immediately ELIMINATED, using the same system of kill that we use against the drug dealers on boats at Sea,” he wrote on social media.

Arsenio Dominguez, the head of the International Maritime Organization, the U.N. agency responsible for shipping safety and security, said on Monday that the naval blockade was in violation of international law. He said at a news conference in London that countries “don’t have the right to blockade an international strait that is used for international navigation.”

He added that a U.S. blockade “just doesn’t really help anything in finding a solution to the conflict,” adding that he was waiting to hear more details about the action.

Mr. Dominguez said that the situation in the region of the Strait of Hormuz remained of grave concern, with 20,000 seafarers on 1,600 vessels stranded in the Persian Gulf.

“There’s the constant threat that a ship may be targeted or attacked, which, of course, endangers lives for the seafarers,” he said. The disruptions to international shipping have also had major consequences for the global economy and food security, he said.