The exchanges came a day after Yemen's Iran-aligned Houthis said they would impose a naval blockade on Saudi Arabia, opening a potential new front in the war and raising the threat to global energy supplies.
Despite the escalating cycle of attacks that has all but wrecked an interim peace agreement signed in June, signs that Tehran and Washington want to resume diplomacy kept oil prices in check.
US Central Command said it had completed its latest round of strikes on Iran, saying it hit Iranian military command centres, maritime capabilities, missile and drone launch sites, and air defence systems.
Iran responded with renewed attacks across the Gulf, with the Revolutionary Guards saying they targeted infrastructure in Bahrain belonging to US tech company Amazon in retaliation for what they described as a US strike on the construction site of Iran's planned Darkhovin nuclear power plant.
Iranian state media reported that Iranian forces also targeted accommodation facilities used by US military personnel at Bahrain's Sheikh Isa Air Base.
The Iranian army said it launched drone attacks against three US military bases in Kuwait on Tuesday.
The Revolutionary Guards said they attacked a US military site in Jordan.
The United Kingdom Maritime Trade Operations agency said on Tuesday a tanker in the strait reported being struck by an unknown projectile, forcing its crew to abandon the vessel and board a lifeboat.
Also on Tuesday, Iran's Revolutionary Guards said two oil tankers had caught fire after explosions while attempting to transit the southern route of the Strait of Hormuz.
Iran had been pressing the Houthis to close the Bab el-Mandeb gateway to the Red Sea if the US continued to attack Iranian power infrastructure - putting two of the world's most vital energy arteries at risk.
A full closure of Bab el-Mandeb would reduce global oil supply by seven per cent as it would leave most Saudi oil exports unable to leave the region, adding to the huge cut to oil flows from the war in the Gulf, which has already reduced shipments by 10 per cent of global supply.
After the Houthis announced their blockade, the Saudi-led coalition in Yemen said it began implementing protection measures for its ships moving through the Bab el-Mandeb Strait.
A senior Iranian official told Reuters on Monday that Tehran had received a proposal from mediators for a 10-day ceasefire in efforts to salvage the interim deal, intended to pave the way to a lasting agreement to end the war that began on February 28 with US-Israeli attacks on Iran.
Iranian Interior Minister Eskandar Momeni has arrived in Islamabad for further talks after asking Pakistan to resume its mediation role in the conflict.
The latest phase of fighting has proved to be among the deadliest of the conflict for US forces. US troop deaths rose to 17 at the weekend.
Trump, under mounting pressure at home over rising petrol prices since the war began, said the latest US strikes on Iran were honouring the deaths of American service members.
"Every time Iran kills an American Soldier they will pay for that killing many times over!" Trump wrote on Truth Social on Monday.
The war has killed thousands of people, mostly in Iran and Lebanon.
Parts of Lebanon remain under Israeli occupation following attacks on Israel by Hezbollah fighters, who said they were acting in solidarity with Tehran.
Lebanese President Joseph Aoun is due to meet Trump at the White House on Tuesday to present a plan on how to disarm Iran-aligned Hezbollah and secure an Israeli withdrawal.
