The two-day-old ceasefire has halted US and Israeli air strikes on Iran, but it has done nothing to end the blockade of the strait, which has caused the biggest-ever disruption to global energy supplies, or to calm a parallel war waged by Israel against Iran's Hezbollah allies in Lebanon.
Iran was doing a "very poor job" of allowing oil to go through the strait, US President Donald Trump said in a social media post, adding: "That is not the agreement we have!"
Iran, for its part, described the ongoing Israeli attacks on Lebanon as a violation of the truce.
Israeli forces launched the biggest attack of the war hours after the ceasefire was announced, killing more than 250 Lebanese in surprise strikes on heavily populated areas.
Iran says the truce was meant to apply to Lebanon, a position initially supported by Pakistan, which mediated it.
Israel and the United States say Lebanon is not covered by the ceasefire.
But in a shift on Thursday, Israel said it would open separate talks with the Lebanese government aimed at ending the war there and disarming Hezbollah.
The rival accusations of violations appeared unlikely to derail the first planned US-Iranian peace talks, set to begin in the Pakistani capital Islamabad from Saturday.
The Iranian delegation will be led by parliament speaker Mohammad Baqer Qalibaf, while Vice-President JD Vance will lead the Americans.
The ceasefire has brought an expectation that Middle East oil will resume flowing, but in the first 24 hours, just a single oil products tanker and five dry bulk carriers sailed through the strait, which typically carries 140 ships a day.
Although Trump has declared victory, the war did not achieve the aims he set out at the start: to deprive Iran of the ability to strike its neighbours, dismantle its nuclear program and make it easier for its people to overthrow their government.
Iran still possesses missiles and drones capable of hitting its neighbours and a stockpile of uranium enriched near the level needed to make a bomb.
Its clerical rulers, who faced a popular uprising just months ago, withstood the onslaught with no sign of organised opposition.
Iran's agenda at the talks now includes demands for major new concessions, including the end of sanctions, and acknowledgement of its authority over the strait, where it aims to collect transit fees and control access in what would amount to a huge shift in regional power.
Its new supreme leader, Ayatollah Mojtaba Khamenei, yet to be seen in public since taking over from his father who was killed on the war's first day, released a defiant statement saying Iran would demand compensation for all wartime damage.
"We will certainly not leave unpunished the criminal aggressors who attacked our country," he said.
The United States, for its part, wants Iran to relinquish the uranium, forgo further enrichment, give up its missiles and end support for regional allies - years-old demands left over from talks Trump abandoned two days before launching the war.
Israeli Prime Minister Benjamin Netanyahu's announcement on Thursday that he had given instructions to start peace talks with Lebanon as soon as possible marked a shift after he rebuffed Lebanese calls for direct talks.
Israel invaded Lebanon in March in pursuit of Hezbollah after the group fired into Israel in support of Iran.
Fighting continues, with Israel's military striking 10 launchers in Lebanon and Hezbollah launching a missile targeting military infrastructure in Haifa.
The armed group had initially indicated it would pause attacks in line with the ceasefire, but resumed fighting after Wednesday's Israeli strikes.
