Meanwhile, Iran warned the US against any further escalation in the Strait of Hormuz, after a spate of attacks risked reigniting the war.
US President Donald Trump urged Iran to "do the smart thing" and make a deal on Tuesday, saying even as the ceasefire teeters that he did not want to kill more Iranians.
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"They should do the smart thing, because we don't want to go in and kill people. Really don't," Trump told reporters in the Oval Office when asked about Iran.
"I don't want to, it's too tough."
Trump's comments were in contrast to his Defence Secretary Pete Hegseth who warned earlier on Tuesday that any attacks on commercial shipping in the Strait of Hormuz would be met with a "devastating" response.
That warning from the Pentagon came on the second day of a US effort to facilitate the transit of commercial ships through the Strait of Hormuz, which Iran had closed in response to the US-Israeli war against the Islamic Republic.
"We're not looking for a fight. But Iran also cannot be allowed to block innocent countries and their goods from an international waterway," Hegseth told reporters.
"If you attack American troops or innocent commercial shipping, you will face overwhelming and devastating American firepower."
Top US military officer General Dan Caine meanwhile said US forces are ready to resume major combat operations against Iran if ordered to do so.
"No adversary should mistake our current restraint with a lack of resolve," said Caine, who spoke alongside Hegseth.
But both Caine and Hegseth downplayed the hostilities, with the general describing it as "low harassing fire" and the Pentagon chief saying that "right now, the ceasefire certainly holds."
US and Israeli forces launched the war on 28 February, after which Iran effectively closed the Strait of Hormuz, a vital route for oil and gas exports, while American forces later launched a blockade of Iranian ports.
President Donald Trump has indefinitely extended what was initially a two-week ceasefire, but the conflict and its widespread economic fallout remain unresolved.
Warning from Iran
Meanwhile, Iran's powerful chief negotiator warned the US against any further escalation in the Strait of Hormuz, after a spate of attacks risked reigniting the war.
The US military said its Apache and Seahawk helicopters hit six Iranian boats threatening commercial shipping and its forces repelled missile and drone attacks on Monday, while the UAE reported fresh Iranian attacks on its territory.
Iran's latest warning followed US President Donald Trump announcing a plan to guide ships from neutral countries out of the Gulf, before the rivals traded fire as they vie for control of the waterway with duelling maritime blockades.
"We know full well that the continuation of the status quo is intolerable for America; whilst we have not even started yet," Mohammad Bagher Ghalibaf, also the speaker in Iran's parliament, wrote in a post on X.
Ghalibaf said the actions of the US and its allies had put shipping security at risk, but said their "malign presence will diminish," with Tehran vowing not to surrender control of the Hormuz.
It denied any of its combat ships had been hit in US attacks but accused Washington of killing five civilian passengers on boats.