US President Donald Trump says an agreement with Iran has been "largely negotiated" and details will be announced soon.
The deal would include the reopening of the Strait of Hormuz, he said on Saturday, without giving further details.
Iranian foreign ministry spokesman Esmaeil Baqaei earlier told state television that US and Iranian positions had been converging in the last week, but warned that did not mean agreements would be reached on key issues and accused the Americans of "contradictory statements".
On social media, Trump said he had a "very good call" with the leaders of Saudi Arabia, the United Arab Emirates, Qatar, and others about a "Memorandum of Understanding pertaining to PEACE".
"An agreement has been largely negotiated, subject to finalization between the United States of America, the Islamic Republic of Iran, and the various other Countries, as listed," Trump said.
"Final aspects and details of the deal are currently being discussed, and will be announced shortly."
He also said he had a call on Saturday with Israeli Prime Minister Benjamin Netanyahu, which "went very well".
The president has not given any further details on the deal, but has insisted any agreement would "absolutely" prevent Iran from obtaining a nuclear weapon.
The US and Israel launched wide-ranging strikes on Iran on 28 February, sparking conflict across the Middle East. Iran responded by launching attacks on Israel and US-allied states in the Gulf.
A ceasefire in Iran was agreed in early April, and since then Washington and Tehran have engaged in talks over a long-term peace deal.
Speaking to state television on Saturday, Iranian foreign ministry spokesman Esmaeil Baqaei also described a "memorandum of understanding", saying Iran's intention was to reach an agreement "in the form of a framework, consisting of 14 points".
Baqaei said they were in the process of finalising the memorandum, so further talks could be held within 30 to 60 days "and ultimately a final agreement can be reached".
The new sense of momentum comes after the mood appeared to have soured in Washington, with anonymous officials briefing US media on Friday that the administration was preparing for a fresh round of military strikes, although no final decision had been made.
On Friday, the president posted on Truth Social that he would not attend his son Donald Jr's wedding this weekend so he could remain in Washington DC "during this important period of time".
Last week, Trump had said the truce was on "massive life support" after rejecting Tehran's demands, labelling them "totally unacceptable".
The US has blockaded Iranian ports since 13 April.
On Saturday, US Central Command (Centcom) said it had redirected 100 vessels, disabled four, and allowed 26 humanitarian aid ships to pass since the blockade began.
Centcom commander Admiral Brad Cooper said its forces had been "highly effective" in "allowing zero trade into and out of Iranian ports which has squeezed Iran economically".
Meanwhile, Iran has claimed military control of an area around the Strait of Hormuz, and has said all transit through the strait "requires coordination with and authorisation from the Persian Gulf Strait Authority".
The US and Gulf allies have repeatedly rejected Iranian attempts to assert control over the strait, and the US has told ships not to comply with Iran's rules.
