US President Donald Trump warned Iran on Monday (Jul 20) that it would pay "many times over" for every American soldier killed as a top Iranian leader said the conflict has escalated into a "full-scale war".

As the United States announced a new round of strikes against the Islamic Republic, Tehran's Yemeni allies, the Houthi rebels, threatened to broaden the war even further by announcing they would blockade Saudi 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 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 United States attacked Iran in late February.

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".

Trump issued his latest warning to Tehran in a post on Truth Social following the deaths of three more US soldiers, bringing the total number of confirmed American fatalities in the war to 17.

Nearly 100 US servicemembers have been wounded since Jul 7, the Pentagon said on Monday, most with minor concussions.

"Every time Iran kills an American Soldier they will pay for that killing many times over!" Trump said. "This directive has been passed on to Secretary of War, Pete Hegseth, Chairman of the Joint Chiefs of Staff, Daniel Caine, and every Leader in the Military."

US Central Command said US forces launched a new round of strikes on Iran on Monday "designed to further degrade Iranian military capabilities used to attack commercial shipping in the Strait of Hormuz".

As Trump ramped up his threats, Iranian President Masoud Pezeshkian said the conflict with the United States has entered a new phase.

"The reality is that today the Islamic Republic of Iran is engaged in a full-scale war," Pezeshkian said.