Iran is reviewing a proposed agreement with the US to halt their war but has not communicated with Washington for a few days, Iranian media reported on Tuesday, after US President Donald Trump said negotiations were ongoing. More than three months after the US and Israel launched strikes against Iran, the conflict has morphed into a stalemate with the pivotal Strait of Hormuz largely shut. Iran has not yet responded to a proposed final text of a temporary deal, and was taking a "stern" approach given what it sees as a history of US non-compliance and longstanding mistrust, Mehr News Agency cited a source as saying. The semi-official Fars agency, also citing a source, added that messages on the possible deal, or memorandum of understanding, had stopped a few days ago, with the last one being Tehran's "clear message" over Lebanon, where Iran is seeking a stop to Israel's incursion against its ally Hezbollah. Trump said on Monday that negotiations were continuing and there would be a deal over the next week to extend a ceasefire agreed in early April and reopen the strait. Since mid-March, he has repeatedly said he is close to a deal, which would postpone thorny issues including the future of Iran's nuclear program. A ceasefire has largely held since early April, but Iran and the US have exchanged strikes several times over the past week. Oil prices fell more than 1% on Tuesday. A senior International Energy Agency official warned that oil inventories could hit historically low levels. ISRAEL KEEPS UP STRIKES IN LEBANON The war that began on February 28 has killed thousands of people, mainly in Iran and Lebanon. It has caused global pain by pushing up energy prices since Iran effectively closed the Strait of Hormuz, which previously carried about a fifth of global supplies of oil and liquefied natural gas. It also triggered the latest round of conflict between Israel and Lebanese group Hezbollah, with Israel pursuing its deepest incursion into Lebanon in 25 years. On Tuesday, Israel kept up strikes on a string of towns in southern Lebanon, Lebanese security sources said, despite a US-mediated partial ceasefire announced on Monday. That would entail Israel refraining from strikes on Beirut and Hezbollah-controlled southern suburbs of the Lebanese capital, while the Iran-aligned group would halt attacks on Israel. But the announcement failed to reassure many Lebanese, 1.2 million of whom have been displaced, and the din of an Israeli drone over Beirut kept residents on edge on Tuesday. "Every time we return to our homes, there is a warning for us to be displaced again," said Faten Al-Chehime, who fled to a displacement camp from her home in Beirut's southern suburbs on Monday, only two weeks after returning there. Israeli Prime Minister Benjamin Netanyahu is facing criticism domestically over any agreement to hold back from further attacks on Beirut, ahead of an election later this year he is projected to lose. IRAN PUSHES FOR LIMITED DEAL In the wider war, Iran is pushing for a limited interim agreement as it tries to ease economic pressure while avoiding major concessions on its nuclear program, according to Iranian sources. Tehran is seeking an end to hostilities across all fronts including Lebanon, access to billions of dollars in oil revenues, waivers on crude exports, a lifting of a US blockade on its ports, and continued leverage over the strait. Trump is under pressure to reopen the strait and curb US fuel prices while not making concessions to Iran. John Bolton, who served as Trump’s national security adviser in his first term and has since become a critic, said the president faced few good options. "I think he wants to have a deal that opens the Strait of Hormuz, and he can declare victory and get the price of gasoline down," Bolton told Reuters. "But he knows if he makes a bad deal, he'll be justifiably criticized for it, so he's between a rock and a hard place, and he doesn't know what to do." Iran's Revolutionary Guard Corps said on Tuesday that 24 vessels had transited the strait in the past 24 hours, after obtaining permission from the Guard's navy. Iran threatened on Monday to expand its blockade to the Bab el-Mandeb Strait, another chokepoint at the mouth of the Red Sea, if Israel resumed strikes on Beirut. Highlighting the risk at sea, the world's largest shipping group MSC said on Tuesday that one of its vessels was struck by two projectiles while in Iraq's Umm Qasr port the previous day. The Revolutionary Guards claimed responsibility for the attack, saying it was carried out in retaliation for a US attack on an Iranian vessel in the Gulf of Oman. The wide-reaching impact of the crisis was laid bare by UN children's agency UNICEF, which said surging transport costs and supply chain disruptions were hindering life-saving aid for Gaza, Lebanon, Democratic Republic of Congo, Mali, Somalia, South Sudan, Nigeria and elsewhere.