The US wants Iran to publicly state that the Strait of Hormuz is open and to pledge to stop firing on commercial ships as part of negotiations due to be heldin Oman on Saturday.
US media cited unnamed officials as saying Tehran had privately acknowledged to President Donald Trump's advisers that the shooting at ships was a mistake, though the Iranians reportedly pinned the blame on a rogue internal group.
Trump has said both sides have agreed to continue talks despite this week's fighting over the Strait of Hormuz, which the White House saw as a violation of the ceasefire.
Iranian Foreign Minister Abbas Araqchi said his country had "kept its word" on the ceasefire, saying on X the US had violated the deal.
In June, the US and Iran signed a ceasefire agreement where Iran would, in part, give safe passage to commercial ships.
Tehran said that an "errant" sect of hardliners was trying to undermine negotiations by firing on the commercial ships, senior US officials told CBS News, the BBC's US partner.
One official told the TV network: "They [the Iranians] came back to the table and said, 'We screwed up. We made a mistake. Let's keep talking.'"
Vice-President JD Vance, Secretary of State Marco Rubio and two people who have been heavily involved in Middle East talks - special envoy Steve Witkoff and Trump's son-in-law Jared Kushner - are expected to lead Saturday's negotiations.
Araqchi is also expected to attend the talks.
In a briefing for reporters on Friday, the US officials said a message to Tehran's leadership had been conveyed through regional mediators demanding Iran release a statement declaring the strait open and that it will stop shooting at commercial ships, according to multiple media reports.
"They're either going to give us that statement or we're not having a good outcome for them," said one official, quoted by Reuters news agency.
The White House also wants Iran to publicly acknowledge that firing on the shipping was a mistake, CBS reports.
Meanwhile, a delegation from Qatar travelled to Iran on Friday for talks aimed at defusing tensions and easing navigation through the Strait of Hormuz.
Trump wrote in a post on Truth Social earlier on Friday: "The Islamic Republic of Iran has asked us to continue 'talks.'
"We have agreed to do so, but the United States has stated to them, in no uncertain terms, that the Cease Fire is OVER!"
In the early hours of Saturday, Trump also responded to reports that Iran had plans to assassinate him.
Writing on Truth Social, he said that the US army would "completely decimate and destroy all areas" of the country in retaliation to such an attack.
The Wall Street Journal and other US media reported this week that Israel had shared intelligence with Washington that Iran had recently devised a plan to assassinate the US president.
There were also open calls for Trump's death at the funeral of Iran's late Supreme leader Ayatollah Ali Khamenei.
Khamenei, who was buried this week, was killed in an Israeli strike on his residence in Tehran on 28 February, the first day of Iran's war with the US and Israel.
No fresh attacks were reported on Friday after fighting broke out in the Gulf region earlier this week, marking the worst exchange of fire between the US and Iran since the two nations signed an interim deal in June.
Three ships were struck while using a US-recommended route through Omani waters. Iran has repeatedly said the only "safe" passage is a separate route through its waters.
Overall progress came last month when the US and Iran agreed on a 14-point memorandum of understanding, which was aimed at extending a ceasefire and ending conflict "on all fronts".
As part of the agreement Iran and Oman must hold talks "to define the future administration and maritime services" in the strait with other Gulf states.
During the conflict, Iran sought to assert its sovereignty over the strait, including by establishing the "Persian Gulf Strait Authority", which it said would manage "safe passage permits".
Iran's Fars news agency has reported that under the new deal with the US the strait would ultimately be managed by Iran in co-ordination with Oman, including possible "service fees" for ships to transit the waterway.
