Tehran said diplomatic messages were still being exchanged by both sides through intermediaries, despite a collapse of a ceasefire.
Late on Monday, Jordan’s military said it had shot down three Iranian missiles, as sirens sounded across the country warning of incoming fire.
Kuwait’s armed forces earlier said they had intercepted Iranian drones.
Bahrain said drones launched by Iran had targeted its air navigation systems, but traffic remained unaffected.
On the US strikes, Iran’s semi-official Tasnim news agency reported that several cities had been hit including Tabriz, Chabahar, Konarak, Bandar Mahshahr and Bandar Imam Khomeini.
There were also Iranian state media reports that two oil tankers had exploded as the vessels tried to cross the strait.
Iran’s Islamic Revolutionary Guard Corps (IRGC) said the tankers were going through what it called an “unsafe and hazardous southern route” of the strait and “exploded and were brought to a halt”.
US Central Command (Centcom) disputed the claims.
The IRGC added that the strait “will not be safe for the transit of petrochemical products, nor even a single drop of oil and gas” as long as the US strikes continue and that it will respond with a “punitive operation”.
Over the weekend, the US confirmed that a service member had been killed after an Iranian attack in northern Iraq on Saturday.
That news came after the US said a separate attack on a base in Jordan on Friday had killed two soldiers there. The two have now been identified by the Pentagon as Pte Isabella Gonzales, 19, and Lt Tyler James Feehan, 25.
A third service member was declared missing after the attack in Jordan, and US officials say “unidentified remains” have been found during the search process.
As the strikes continued over the weekend, US Secretary of State Marco Rubio said that the US “always remains open to a diplomatic solution”.
He also said “the world has to decide whether or not it’s going to allow an international waterway to be under the control” of Iran, saying Tehran was using the crucial shipping route as leverage.
His comments come as a preliminary deal made in mid-June to stop fighting has unravelled, with negotiations for a permanent peace making little progress after Trump declared the agreement was “over” on 8 July.
