Donald Trump said the Strait of Hormuz would open "very soon" or Iran would be "hit very hard" as oil prices fell to a three-week low amid hopes of a deal.
The US president was speaking to Fox News after Secretary of State Marco Rubio and Treasury Secretary Scott Bessent both said talks had progressed to allow shipments potentially to resume later this week.
The cost of a barrel of Brent crude, the global benchmark for oil prices, fell by almost 5% to under $80 (£60) on the news of supply disruptions potentially being eased.
But the failure of previous talks in recent months to de-escalate the conflict has led to a volatile oil market, with motorists ultimately being hit by higher fuel prices.
"We're having very good discussions," Trump said during a visit to California, insisting Iran was keen to seal a deal to bring an end to months of conflict.
US Central Command (CentCom) said the "southern route through the Strait of Hormuz remains free and open for all commercial vessels seeking to transit the international waterway".
On Tuesday, along with the drop in Brent crude, US West Texas Intermediate prices were down more than 5%, to $76 a barrel. Both contracts dropped to their lowest levels since 13 July.
Rubio said there had been progress made in discussions on getting more ships through the strait with Iran and Oman.
"There's been progress made in those talks, but not finality yet. We're hoping that will happen very shortly," he told reporters at the State Department.
Bessent said a deal to reopen the Strait of Hormuz could be agreed as soon as Tuesday or Wednesday.
There was a "chance we may have a deal today or tomorrow to open the strait and move towards a more normalised position in this conflict," he told CNBC.
"It would be freedom of movement," he added, when asked whether Iran would be allowed to charge for ships passing through.
While senior figures in the US government have announced talks have been progressing, no details of what a potential deal may look like have been released.
Iran has said it is not negotiating with the US - and has no plans to do so - and is instead talking to Oman.
A spokesman for Iran's foreign ministry said that talks with Oman, a mediator in negotiations, on a new mechanism for vessels going through the Strait, had been positive.
Qatar, which is a key mediator between Washington and Tehran, said it was continuing efforts with other mediators to try to achieve a diplomatic resolution to the war, but admitted no direct talks were currently planned.
With the conflict continuing to drag on, the US has used nearly all of its global stockpile of long-range precision missiles, two sources with direct knowledge of the matter told the BBC's US news partner CBS News.
The Strait of Hormuz has been a central point in negotiations between the US and Iran. Before the conflict began in late February, the waterway handled about one-fifth of global daily oil and liquefied natural gas supplies.
Iran has halted most traffic through the Strait since the conflict began, while the US has also imposed a naval blockade of Iranian ports in the region.
Another blockade is in place on Saudi Arabia's ports in the Red Sea, imposed by Yemen's Iran-backed Houthis since 20 July.
The route had become a crucial alternative since Iran blocked the strait, but it has become increasingly dangerous, with a spate of attacks on vessels reported in the past week.
On Tuesday, a projectile sank an Indian-flagged vessel near Yemeni waters, the India's shipping minister said, with all 14 on board rescued.
Analysts believe the threat to ships carrying oil in the Middle East is at its worst since the Iran war started.
"Investors are acutely aware of how many times we've already been at this point in the war and how fragile the process of securing lasting agreements can be," said Danni Hewson, head of financial analysis at AJ Bell.
The disruption has sent prices at the pumps up across the world. In the UK petrol prices are now at levels seen at the start of the conflict, with the average cost of a litre of petrol hitting £1.60, according to the RAC motoring group.
In the US, gasoline prices are on average above $4 a gallon, according to the AAA. Diesel is almost $5.40 a gallon.
Prices have surged to above $120 when the conflict has escalated and plunged in response to previous talks suggesting a breakthrough.
The elevated prices have led to major oil companies, such as BP, Shell, Chevron and Exxon Mobil, to report bumper profits.
However, Hewson added that despite the huge revenues, oil companies were "at the mercy" of US President Donald Trump's "machinations".
On Monday, Trump warned Iran faced its "last chance" to agree a deal to allow commercial shipping to resume in the Strait.
He said he had called off "massive" strikes on the country for talks to resume.
US stock markets were trading higher on Tuesday following news of the negotiations lowering oil prices and also in response to corporate results related to Artificial Intelligence.
Investors have experienced jitters on Wall Street as results from Big Tech firms indicate spending on the technology is set to continue to soar.
Source: BBC
– Agencies
