US Secretary of State Marco Rubio says US and Iranian negotiators have "a pretty solid thing on the table" and a deal to end the war between the two countries may be reached on Monday.
"We're still a work in progress," Rubio said during a visit to India.
He was speaking after President Donald Trump said he had instructed negotiators "not to rush into a deal", after earlier suggesting one was close.
It reportedly involves a 60-day ceasefire extension, reopening the Strait of Hormuz and a plan for further negotiations over Iran's nuclear programme.
Oil prices fell sharply and Asian stock markets rose on Monday on hopes of an agreement.
"We're still a work in progress. As I said, you know, we thought we might have some news last night. Maybe today," Rubio said on Monday in the Indian capital, Delhi.
"So we have, what I think is a pretty solid thing on the table in terms of their ability to open up the Straits," he said referring to the Strait of Hormuz - the crucial waterway where 20% of the world's oil and liquefied natural gas passes and which Iran has been blocking.
Cautioning "I wouldn't read too much into it", Rubio said "it takes a little while to hear back from Iran".
CBS News, the BBC's US partner, has reported that US intelligence believes Iran's supreme leader - who was injured in an Israeli strike on the first day of the war - is holed up in an undisclosed location, making communication with his envoys difficult and therefore delaying pace of talks with the US.
Iran's foreign ministry spokesperson Esmail Baghaei said at the weekend the two sides were both "very close and very far" from reaching an agreement.
According to US media, the mooted deal is not a final settlement and instead leaves some of the thorniest issues to be negotiated later, including the scope and timing of Iranian sanctions relief, the release of frozen Iranian funds, and Washington's demands for Iran to curb its nuclear ambitions.
The reported deal has split Trump's Republicans, with some publicly arguing it is too lenient on Iran.
Senator Ted Cruz said it would be "a disastrous mistake", while Roger Wicker, who chairs the Senate Armed Services Committee, said a 60-day ceasefire would mean "everything accomplished by Operation Epic Fury would be for naught!"
Senator Lindsey Graham, who is a close Trump ally, also criticised any deal that would leave Iran perceived as being a dominant force in the region.
"It makes one wonder why the war started to begin with," he said.
Trump responded by saying he did not "listen to the losers, who are critical about something they know nothing about".
"If I make a deal with Iran, it will be a good and proper one," he wrote on Truth Social.
The US and Israel launched wide-ranging strikes on Iran on 28 February, sparking conflict across the Middle East. Iran responded by attacking Israel and US-allied states in the Gulf, and effectively closed the Strait of Hormuz. The move sent oil prices soaring globally.
Shortly after a ceasefire was agreed in early April, the US established a blockade of Iranian ports, which Trump says will remain "in full force and effect until an agreement is reached, certified, and signed".
In Sunday's post on Truth Social, Trump reiterated that Iran "must understand" it cannot develop a nuclear weapon. Tehran has repeatedly said its nuclear programme is solely for peaceful purposes.
Some reports in US media suggest the deal could see Iran agree to eventually hand over its highly enriched uranium.
At the start of the war, Iran is thought to have had about 440kg (970 lbs) of uranium that was enriched up to 60% purity - a short process away from being enriched further to the weapons-grade 90%, which theoretically could allow it to create a nuclear bomb.
Iranian President Masoud Pezeshkian told state TV Iran was ready "to assure the world that we are not after a nuclear weapon."
