The talks are based on a 14-point interim accord signed last month that was meant to halt the war that began with US-Israeli strikes on Iran in February and reopen the strait, while setting up 60 days of negotiations for a permanent peace deal.
However, the US and Iran have sparred publicly over the meaning of the interim pact, leading to tit-for-tat military strikes over the past week and leaving little sign of progress on more complex issues, including on Iran's nuclear program.
Iran is determined to win international recognition of its control over the strait and its ability to levy fees on ships entering or leaving the Gulf, even if it has to do so by force, according to two senior Iranian sources.
Traffic has partially resumed through the waterway, which handled one-fifth of global oil and liquefied natural gas trade before the war.
US President Donald Trump, who has said removing Iran's highly enriched uranium is a top priority, told reporters on Wednesday that "the denuclearisation of Iran is moving along well", without giving details.
"They've had very good meetings, and we'll see," he said of the talks in Doha, where there was no evidence the nuclear issue had yet been discussed.
The indirect talks, mediated by Qatar and Pakistan, began on Tuesday night and were continuing on Wednesday, the Iranian official said.
They are structured as sessions between chief negotiators and specialists, the source with knowledge of the talks said, adding that Trump's son-in-law Jared Kushner and envoy Steve Witkoff met Qatar's prime minister to lay groundwork for the talks but would not be attending.
Kushner and Witkoff later met Qatar's emir to discuss US-Iran negotiations and developments in Lebanon, where a parallel conflict between Israel and Iran-backed militant group Hezbollah erupted in early March.
Iran's Deputy Foreign Minister Kazem Gharibabadi headed a delegation of representatives from Iran's foreign ministry, central bank and agriculture ministry, meeting Qatar's prime minister and holding talks with mediators.
Iran has stated publicly that its priorities include agreeing on management of the strait and the release of $US6 billion ($A8.7 billion) in Iranian frozen assets, and the Iranian official said the current round of discussions would focus on those two issues.
The stated priority of the US is to ensure the free flow of traffic through the strait, the source with knowledge of the talks said.
Iran's state media said on Wednesday a foreign container ship had run aground in the Strait of Hormuz after entering shallow waters outside the shipping route designated by Iranian authorities.
"Hormuz continues to reopen but it's patchy, unpredictable, and not fully transparent," said Vandana Hari, founder of oil market analysis provider Vanda Insights.
The war triggered Iranian attacks on Gulf states hosting US military bases and killed thousands of people, mainly in Iran and Lebanon, as well as pushing up oil and fuel prices.
Trump faces domestic pressure to contain the economic fallout from the war before midterm elections in November, as well as criticism from his own party that the interim deal leaves US objectives unmet.
In Iran, the theocratic leadership survived the war but faces domestic anger over a shattered economy. Oil prices dipped further on Wednesday, with US West Texas Intermediate crude reaching its lowest since February 27 - a day before the war's outbreak - at just under $US69 ($A100) a barrel.
The interim deal between the US and Iran also provides for an end to the conflict in Lebanon. The US has backed a separate track of talks between Israel and Lebanon's government, which produced a framework security deal that Hezbollah has dismissed and analysts warn could entrench Israel's occupation of Lebanon's south.
There had been intensive diplomatic activity on Lebanon between parties including the US up to Tuesday evening, the source with knowledge of the talks said.
