Washington believes it is close to reaching an agreement with Iran to reopen the Strait of Hormuz and end the war, US news outlet Axios reported Wednesday, citing two US officials.
According to Axios, the two sides are close to agreeing on a "one-page memorandum of understanding to end the war and set a framework for more detailed nuclear negotiations."
It said the deal would involve Iran committing to a moratorium on nuclear enrichment and the United States agreeing to release billions of dollars of frozen Iranian funds.
Washington is reportedly awaiting a response from Tehran on several key points in the next 48 hours.
"Nothing has been agreed yet, but the sources said this was the closest the parties had been to an agreement since the war began," Axios said.
US President Donald Trump has repeatedly said that an agreement is close, without ever reaching one.
Trump launched "Project Freedom" on Monday to help vessels leave the strait.
But he suspended the operation after just one day following requests from "mediator Pakistan and other countries," saying "Great Progress has been made toward a Complete and Final Agreement" with Tehran.
The one-page, 14-point memorandum of understanding was being negotiated between US envoys Steve Witkoff and Jared Kushner and several Iranian officials, both directly and through mediators, Axios said.
In its current form, the memorandum would declare an end to the war in the region and the start of a 30-day period of negotiations on a detailed agreement to open the strait, limit Iran's nuclear programme and lift US sanctions, Axios added.
The mission had failed to bring about any significant resumption of traffic through the waterway, while provoking a new wave of Iranian strikes on ships in the strait and on targets in neighbouring countries.
In the latest incident, a French shipping company reported on Wednesday that one of its container ships had been struck in the strait the previous day, and that the injured crew had been evacuated.
Trump had launched the naval mission to guide ships through the strait after saying he was likely to reject Iran's latest proposal. The Iranian offer, made last week, also contained 14 points.
It had called for setting aside discussion of nuclear issues until after the war ended and the shipping dispute was resolved.
In comments on a visit to China on Wednesday, Iran's Foreign Minister Abbas Araqchi made no mention of Trump's latest remarks, but said Tehran was holding out for "a fair and comprehensive agreement".