Israel's cabinet met on Wednesday to discuss a possible ceasefire in neighbouring Lebanon, a senior Israeli official said, more than six weeks into its war with Iran-backed Hezbollah.
Trump said talks between leaders of both countries would take place on Thursday, while the Financial Times reported a ceasefire could be announced soon, citing Lebanese officials.
Ending the fighting in Lebanon was a key sticking point in earlier peace talks, along with how to deal with Tehran's nuclear ambitions.
US and Iranian officials were weighing a return to Pakistan for further talks as early as the coming weekend, after negotiations ended on Sunday without a breakthrough.
Pakistan's army chief and key figure in the mediation, Field Marshal Asim Munir, arrived in Tehran on Wednesday to try to prevent a renewal of the conflict.
"We feel good about the prospects of a deal," White House press secretary Karoline Leavitt said at a news conference on Wednesday, calling conversations mediated by Pakistan "productive and ongoing".
Pakistan's military confirmed Munir had arrived in Tehran. A senior Iranian source told Reuters that Munir, who had mediated the last round of talks, would seek "to narrow gaps" between the two sides.
Iranian Foreign Minister Abbas Araqchi posted on X welcoming Munir and said Tehran was committed to "promoting peace and stability in the region".
The talks last weekend broke down without an agreement to end the war, which Trump began alongside Israel on February 28, triggering Iranian attacks on Iran's Gulf neighbours as well as reigniting the Israel-Hezbollah conflict.
Thousands of people have been killed, mostly in Iran and Lebanon, while soaring energy costs have rattled investors and policymakers around the world.
Stock markets have rallied strongly in recent days on expectations of a swift resolution to the fighting, with indexes on Wall Street hitting record highs on Wednesday as crude oil prices steadied.
"While there are hopes for de-escalation, many investors remain sceptical, given that US-Iran talks have repeatedly broken down even after appearing to make progress," said Toshitaka Tazawa, an analyst at Fujitomi Securities.
Treasury Secretary Scott Bessent predicted China's purchase of Iranian oil would "pause" given a US blockade on vessels calling at Iranian ports. He said the US could impose secondary sanctions on countries that purchase Iranian crude.
The US Treasury had warned two Chinese banks not to process Iranian money or face sanctions, he said, without naming the banks. China previously bought more than 80 per cent of Iran's shipped oil.
Trump said on Wednesday he had told Chinese President Xi Jinping not to give Iran weapons, which Xi had said he wasn't. Trump also said China was very happy he was "permanently opening" the Strait of Hormuz.
"I am doing it for them, also - And the World," he wrote on social media, adding: "President Xi will give me a big, fat, hug when I get there in a few weeks."
The war has led Iran to effectively shut the Strait - a vital artery for global crude and gas shipments - to ships other than its own, sharply reducing exports from the Gulf and leaving energy importers scrambling for alternative supplies.
During the first 48 hours of the US blockade on ships entering and exiting Iranian ports, no vessels have made it past US forces, the US military said.
Additionally, nine vessels complied with direction from US forces to turn around and return toward an Iranian port or coastal area.
However, Iran's Fars News agency said an Iranian supertanker subject to US sanctions crossed the strait towards Iran's Imam Khomeini port despite the blockade. Fars did not identify the tanker or give further details of its voyage.
Iran's joint military command warned it would halt trade flows in the Gulf, the Sea of Oman and the Red Sea - which connects to the Suez Canal - if the US blockade continued.
Trump has also threatened to escalate if the war resumes.
"We could take out every one of their bridges in one hour. We could take out every one of their power plants, electric power plants, in one hour. We don't want to do that...so we'll see what happens," he told Fox Business Network.
Iran's nuclear ambitions were a key sticking point at last weekend's talks.
