The report said the US would end a naval blockade of Iranian shipping, citing a memorandum of understanding being negotiated between the two sides to end the war which has choked global energy supplies through the strategic waterway.
Iranian state TV said it had obtained an unofficial draft of the MOU though it was not final and may not be agreed.
State TV said the framework, which excludes military vessels and envisages Iran managing ship traffic through the strait in co-operation with Oman, was not yet finalised and that Iran would take no steps without "tangible verification".
The US denied the report, saying it was "complete fabrication" in a White House statement on social media.
Iran's government did not comment.
The issue of US troops in the region also needs further discussion, the TV report said without being more specific.
There was no mention of Iran's nuclear program which the US wants disbanded.
US Secretary of State Marco Rubio said on Tuesday it may take a few more days, after President Donald Trump had raised hopes over the weekend for an imminent end to the war.
Key sticking points have included reopening and management of the waterway through which a fifth of the world's oil and liquefied natural gas flowed before the conflict and the dismantling of Iran's nuclear capacity.
Oil prices fell more than five per cent on Wednesday after the Iranian TV report.
It was not immediately clear what a US military pullback as described by Iranian state television would look like.
The US military has about 15,000 troops enforcing a blockade of Iran and has thousands of additional forces at bases throughout the region, including in Gulf states like Qatar, the United Arab Emirates and Bahrain.
US naval vessels regularly transit the region, stopping in ports including in Oman.
Iranian sources have said talks on the nuclear issue will come in a second round of negotiations - something that may not be acceptable to some of Trump's closest supporters.
Trump, who will meet with his top aides at the White House on Wednesday, has said dismantling Iran's nuclear program to prevent it from developing a nuclear weapon was the key aim of the war.
Iran says the program is for peaceful purposes only.
with AP
