Trump had previously said the deal would include the reopening of the key Strait of Hormuz shipping route, without giving further details.
The Strait of Hormuz, through which around a fifth of the world’s oil and liquefied natural gas (LNG) usually passes, has been effectively closed since the conflict started on 28 February.
Earlier on Monday, Rubio said the talks were “still a work in progress.”
“As I said, you know, we thought we might have some news last night,” Rubio said in the Indian capital, Delhi.
His comments came after Trump said he had instructed negotiators “not to rush into a deal”, after earlier suggesting one was close.
Speaking after Rubio’s comments, Iran’s foreign ministry spokesman, Esmail Baqai, said agreement has been reached on a “large portion of the issues under discussion”.
“But to say that this means the signing of an agreement is imminent – no-one can make such a claim,” he added.
On Saturday, Trump said that he had 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 finalisation between the United States of America, the Islamic Republic of Iran, and the various other Countries, as listed,” Trump said on social media.
“Final aspects and details of the deal are currently being discussed, and will be announced shortly.”
He also said he had had a call on Saturday with Israeli Prime Minister Benjamin Netanyahu, which had gone “very well”.
On Monday, Trump said in his discussions with the Gulf leaders and others, including the presidents of Turkey and Egypt, he pushed them to sign the Abraham Accords which are aimed at normalising relations with Israel.
