US President Donald Trump has said Iran is "getting a lot closer" to reaching an agreement with the US on the war, as Tehran also signalled progress had been made in the past week.
However, both sides have been cautious, and Iran's foreign ministry spokesperson said the key issue of nuclear weapons would not be part of any initial proposals.
Trump told the BBC's US partner CBS News he had seen a draft agreement with Iran. When asked whether it was good enough, he said: "I don't know, I can't tell you that."
The president did not give any further details on the draft, but insisted any agreement would "absolutely" prevent Iran from obtaining a nuclear weapon.
"I will only sign a deal where we get everything we want," he said. "We're going to have a deal, or we're going have a situation where no country will ever be hit as hard as they're about to be hit."
Iranian foreign ministry spokesman Esmaeil Baqaei told state television on Saturday that the 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".
"Our plan has been to first draft a memorandum of understanding, or an agreement, in the form of a framework, consisting of 14 points," he said, according to Reuters news agency.
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".
Trump is expected to hold a phone call with leaders from Saudi Arabia, Qatar, the United Arab Emirates (UAE), Egypt, Turkey and Pakistan on Saturday, Reuters reported, citing an Arab official.
Meanwhile, US Secretary of State Marco Rubio was cautiously optimistic during a visit to India on Saturday, and said there could be an update this weekend.
Rubio also emphasised the US's position that Iran must not be allowed a nuclear weapon, and spoke of reopening the Strait of Hormuz without tolls from Iran.
The country also needed to turn over its highly enriched uranium, he said.
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 temporary ceasefire between Iran and the US started in early April.
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.
