US President Donald Trump has predicted that the war in Iran will be "over quickly" and says that most people "understand" his goal of ending Tehran's nuclear ambitions.
His comments come after Iran said a US proposal to end the war is "still being considered".
US news outlet Axios reported that the White House believes it could be closing in on a 14-point memorandum of understanding with Iran, which could set a framework for more detailed nuclear negotiations.
A senior member of Iran's parliament has dismissed it as a "wish list", while a foreign ministry spokesman said Tehran would share its views of a US proposal with Pakistani mediators.
Pakistan's foreign minister said his country was "endeavouring to convert this ceasefire into a permanent end to this war".
In its report, Axios describes the memorandum as a one-page, 14-point memo which could set a framework for more detailed nuclear negotiations.
Among the provisions it lists are a suspension on Iranian nuclear enrichment, the lifting of sanctions, and restoring free transit through the Strait of Hormuz.
It cites two US officials and two other sources - all unnamed - whom it describes as briefed on the issues. These sources are reported as saying that many of the terms laid out in the memo would be contingent on a final agreement being reached.
The Reuters news agency reported that two sources briefed on the mediation between the US and Iran had confirmed the information initially reported by Axios, but the proposal has not been publicly outlined.
Speaking during a virtual campaign event on Wednesday evening, Trump told Republicans in the State of Georgia that he was optimistic that the war would end soon.
He added that most people understood he was right to deny Iran the opportunity to have a nuclear weapon.
Earlier in the day, the president said the US has had "very good talks with Iran in the last 24 hours" and that was deal is possible, emphasising that any hardship caused to Americans - because of high fuel prices - would be short term.
Ealier, Iranian foreign ministry spokesperson Esmail Baghaei told the Iranian Students' News Agency (ISNA): "The American proposal is still being reviewed by Iran and after concluding, it will inform the Pakistani side of its opinion."
Responding to the Axios report, Ebrahim Rezaei, the spokesperson of the Iranian Parliament's national security and foreign policy commission, wrote on X: "The Americans will not gain anything in a war they are losing that they have not gained in face-to-face negotiations."
He also said Iran "has its finger on the trigger and is ready" and warned that if the US did not "surrender and grant the necessary concessions", Iran would "deliver a harsh and regret-inducing response".
Trump has threatened renewed violence as well, writing on his Truth Social platform that if Iran did not agree to a deal "the bombing starts, and it will be, sadly, at a much higher level and intensity than it was before".
He also said Operation Epic Fury - the initial US-Israeli offensive in Iran - would come to an end "assuming Iran agrees to give what has been agreed to". That was after US Secretary of State Marco Rubio said the operation was over after achieving its objectives.
Trump also said, not for the first time, that Iran has agreed to never have a nuclear weapon "among other things" - a claim that has not been confirmed by Tehran. Iran's nuclear programme has been one of the key sticking points between the two sides.
"They [Iran] want to make a deal. We've had very good talks over the last 24 hours and it's very possible that we'll make a deal up there," Trump said, adding: "I think we won."
He announced on Tuesday that he was pausing Project Freedom, just days after announcing it. The operation was meant to help restore the flow of oil and the global economy's eventual return to normalcy by guiding stranded ships out of the Gulf through the Strait of Hormuz.
Iran has yet to react publicly to the pause but the Iranian Revolutionary Guard Corps (IRGC) alluded to the strait reopening if there is an "end of the aggressors' threats".
The crucial waterway, through which 20% of the world's oil and liquefied natural gas usually passes, has effectively been blockaded by Iran since the US and Israel began attacking it in late February.
In early April, the US and Iran announced a ceasefire under which Iran ended its drone and missile strikes on Gulf countries including the UAE, but few vessels have been able to transit the strait since then.
The US also imposed its own blockade on Iranian ports, saying it has stopped dozens of ships. US Central Command said on Wednesday it had shot at and disabled an Iranian-flagged oil tanker in the Gulf of Oman that was trying to break the blockade.
Israeli Prime Minister Benjamin Netanyahu said on Wednesday that there was "full coordination" between himself and Trump over Iran.
"There are no surprises. We share common goals, and the most important objective is the removal of all enriched material from Iran and the dismantling of Iran's enrichment capabilities," he said.
His comments came after Israel launched its first strike on the Lebanese capital, Beirut, since a ceasefire was agreed in April.
Netanyahu wrote on social media that forces had targeted a senior Hezbollah commander "responsible for firing at Israeli settlements and harming IDF [Israel Defense Forces] soldiers".
Hezbollah, an Iranian-backed militia and political party, began striking Israel in early March in retaliation for its attacks on Iran.
Despite the ceasefire agreement, Israel and Hezbollah have continued with their attacks, accusing each other of violations.
Most of Israel's air strikes have hit southern Lebanon, while Hezbollah has carried out attacks on Israeli troops in Lebanon and northern Israel with rockets and drones.
