Tehran, Iran - Iran on Tuesday targeted US radar and defense installations, as well as assets in Kuwait and Bahrain, as Houthi rebels in Yemen threatened to widen the conflict with a blockade of Saudi Arabian ports.

Tehran's Islamic Revolutionary Guard Corp (IRGC) said they had attacked and stopped two "non-compliant oil tankers" attempting to transit the Strait of Hormuz, as part of an effort to tighten Iran's grip on the vital waterway.

Following the deaths of at least three US soldiers in the past several days, the US launched a brutal round of attacks on Monday which it said were "designed to further degrade Iranian military capabilities used to attack commercial shipping."

In retaliation, the Iranian army said hours later that it had targeted US assets in Kuwait and Bahrain, including air defense systems, radar installations, and administrative buildings.

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"With this radar sweep, the enemy should prepare for even more decisive and powerful waves of drone and missile attacks," the IRGC said in a statement carried by state news agency IRNA.

"The army's ground forces targeted the HIMARS missile systems of the US terrorist army stationed at the Arifjan base in Kuwait with surface-to-surface missiles," IRNA quoted army officials as saying.

"HIMARS is a mobile missile system with the ability to move quickly against ground targets, which, when targeted, causes damage to the offensive and defensive layers and reduces the enemy's missile power in aggressive crimes."

President Donald Trump warned Monday that Iran would pay "many times over" for every American soldier killed, while Iranian President Masoud Pezeshkian said the conflict had become "a full-scale war."

Meanwhile, Tehran's Yemeni allies, the Houthi rebels, threatened a major broadening of the war with the announcement that they would attempt to blockade Saudi Arabian ports.

Such a move by the Houthis would put at risk Riyadh's ability to bypass the flashpoint Strait of Hormuz for some of its oil exports, and would likely have major repercussions on the global economy.

Saudi Arabia and the Houthis traded fire last week for the first time in years, threatening a 2022 truce, but the rebels have largely remained on the sidelines since Israel and the US launched a war of aggression against Iran on February 28.

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Saudi Arabia strongly condemned the threat from what it called the "terrorist Houthi militia" and said it "continues to support the brotherly Yemeni people and their legitimate government."

Although far below its prewar totals, Saudi Arabia has been able to continue exporting millions of barrels of oil a day via its Red Sea port of Yanbu despite the widening regional conflict.

Oil markets have for months feared that the Houthis would return to attacking shipping in the Red Sea and Gulf of Aden, potentially cutting off yet more crude oil from global markets.

The Houthis, who have been at war with Riyadh for over a decade, have not said how they will enforce their blockade.