US President Donald Trump has signalled progress towards a possible agreement with Iran, as Tehran pushes to accelerate its ceasefire proposal.

“It looks like that’s coming together very nicely,” Trump said on Monday at the Lincoln Memorial Reflecting Pool in Washington, DC. “That’s why I guess the oil prices dropped. People found out about it.”

His comments followed a post on Truth Social in which he said Iran wanted a settlement “as soon as possible”, adding: “It could happen!”

Trump also claimed oil prices had fallen by almost $10 a barrel, attributing the decline to expectations that the war on Iran would end soon.

US Vice President JD Vance said Washington had held “a number of good conversations with the Iranians” and that he and Trump felt optimistic about the prospects for a negotiated settlement.

“We’re going to keep on working at it,” Vance told reporters at Joint Base Andrews.

“We’ve certainly made some progress. We’ll see if we can make some more,” he added.

Asked whether Washington had given Tehran a deadline to reach a deal before Trump resumed strikes, Vance said, “No, we haven’t set deadlines.”

He said Trump retained military and nonmilitary options, and that any agreement required “a firm commitment and a verifiable commitment” that Iran would not rebuild its nuclear programme, which Vance claimed the US had destroyed.

The US remarks came as Iranian officials said their seven-step plan remained unchanged but could now be implemented within two days rather than a week. The proposal includes a swift reopening of the Strait of Hormuz and a return to talks over Iran’s nuclear programme.

Iranian Ministry of Foreign Affairs spokesman Esmaeil Baghaei said the offer had been “condensed and can be implemented within two days”.

“If Iran’s demands are met, it is possible that both security will be restored to the Strait of Hormuz and the negotiation process will begin within a short period of time,” Baghaei said. “All of this depends on how the American side wants to proceed regarding the future of this process.”

Iran’s Supreme Leader Mojtaba Khamenei had granted “powers” to the government to accelerate talks with Washington to end the war, the state IRNA news agency reported.

Minister of Foreign Affairs Abbas Araghchi reiterated that Tehran was prepared for both diplomacy and military confrontation, as Qatar and Pakistan continued to facilitate indirect talks.

“By accepting these conditions, the Strait of Hormuz will be opened, and negotiations will resume,” Araghchi told IRNA in Ashgabat, Turkmenistan. “Otherwise, the current situation will continue, and Iran will not bow down.”

Iran previously said its plan could be implemented within a week if Washington met Tehran’s conditions. They include the US lifting its naval blockade of Iran’s ports, repealing sanctions, guaranteeing an end to strikes, and securing a complete regional ceasefire, especially in Lebanon.

Baghaei gave no indication that Tehran had changed its demands or that Washington had accepted its proposal.

Despite the latest expressions of optimism, Trump has suggested several times that the US could strike Iran after the November 3 US midterm elections.

He told the Right Side Broadcasting Network (RSBN) on Sunday that the war on Iran would end “very soon one way or the other”, adding that Tehran would either “make a deal, or we’ll just end it”.