The Iranian-backed Houthis have claimed a missile attack on Saudi Arabia, after Riyadh launched strikes on targets linked to the group on Friday.
Early on Saturday, the Houthis' Ansarollah media said on Telegram that a "Yemeni missile strike" had caused fires in the Saudi city of Jizan. Saudi authorities had issued emergency alerts for the province.
The group had vowed retaliation after Saudi Arabia launched air strikes on Houthi targets in the Yemeni port city of Hodeida and a nearby island on Friday.
It came as there were no overnight reports of air strikes in the wider region by the US or Iran for the first time in two weeks.
The US military did not announce fresh strikes on Iran on Saturday, having carried out 13 consecutive nights of attacks on the country. During this time, Iran has also launched drone strikes on US military facilities and bases across the Middle East.
Earlier, a delegation from Oman arrived in Iran's capital Tehran for talks on the Strait of Hormuz, Iran's state-run IRNA news agency reported. Oman controls the strait's southern coastline.
Speaking to reporters at the White House on Friday afternoon, Trump continued to threaten further attacks while saying that negotiations were continuing.
"We are talking to them. I think they're being serious. I think ... they are being by far the most serious that we've seen them, but that doesn't mean we get there," he said.
Asked about his exit strategy for the Iran war, Trump said: "There's a military exit where we just keep going just the way we are, and we can even make it a heavier dose, and it's knocking out everything they have. Or there's a smarter strategy that you make a deal."
But he added: "We're locked and loaded. We're ready to go."
In the Strait of Hormuz on Friday, the US military said it had fired on and disabled a tanker ship in the Gulf of Oman that was attempting to evade the American blockade on Iranian ports.
The vessel attacked by the US is the second commercial ship the US has disabled since it reimposed its blockade earlier this month.
"We disabled the tanker after the crew attempted to run the blockade at least four times prior," Navy Captain Tim Hawkins, spokesman for US Central Command, told AFP.
"The crew was repeatedly warned, didn't comply, and US forces on scene disabled the ship after firing into its engine room," he said. "The ship is no longer transiting to Iran."
Growing concern over new threats to shipping in the Red Sea from Yemen's Houthis helped push the price of crude oil back over $100 (£74.96) a barrel this week - the highest level since May.
But it dropped again on Friday afternoon, with Brent futures down more than US$4 (£3.00) to a little over $96 (£72.07), according to the Reuters news agency, which reported the fall occurred after the successful passage through the Bab el-Mandeb Strait by two Chinese-chartered supertankers.
Following the exchange of fire early on Saturday, the Houthis' Ansarollah media posted on Telegram, "The Saudi enemy's targeting of civilian facilities in Hodeida and Kamaran island constitutes a dangerous escalation," adding: "We affirm that these recent crimes will not go unanswered."
Saudi authorities did not immediately respond.
The US and UK are set to hold a conference in London next week to discuss the Strait of Hormuz, the BBC understands. US Defence Secretary Pete Hegseth and Chairman of the Joint Chiefs of Staff Dan Caine will attend the conference, which was first reported by Axios.
It comes as Israeli Prime Minister Benjamin Netanyahu is scheduled to meet the US president at the White House on Tuesday.
In June, the US and Iran agreed on a 14-point Memorandum of Understanding (MOU) to halt military operations and reopen the Strait of Hormuz, as well as to reach an agreement to end the war over the following 60 days.
But three weeks after it was signed, Trump declared the ceasefire "over" after Iranian attacks on ships in the strait, and US strikes in response.
Source: BBC
--Agencies
