US President Donald Trump sent a peace plan to Iran as he voiced optimism Tuesday at ending nearly a month of a war, with Tehran announcing that it will let “non-hostile” oil vessels go through the crucial Strait of Hormuz.

The tentative signs of a diplomatic solution came despite new violence, with an Iranian missile causing injuries in Israel which in turn pressed on multiple fronts and vowed to seize control of a strip of southern Lebanon.

Trump, whose pronouncements in recent days have swung wildly from vowing massive attacks on Iran to declaring the nearly month-long war virtually over, said the United States was “in negotiations right now” with Iran — which has not confirmed any formal talks.

“They did something yesterday that was amazing actually. They gave us a present and the present arrived today. And it was a very big present worth a tremendous amount of money,” Trump told reporters in the Oval Office.

“That meant one thing to me — we’re dealing with the right people.”

He did not explain further but said it related to the Strait of Hormuz, which Iran has largely blockaded in retaliation for US and Israeli strikes, sending global energy prices soaring.

Iran, in a message circulated by the International Maritime Organization shortly afterward, assured safe passage to “non-hostile vessels” going through the strait, the gateway for one-fifth of the world’s oil.

Iran had already in recent days said it was not targeting friendly nations, although many vessels have shied away as insurance companies refuse to take risks.

New nuclear deal? 

Trump had earlier threatened to “obliterate” Iran’s power plants, which some argue would be a war crime, if it did not open the strait by late Monday Washington time. Before US markets opened Monday, Trump abruptly extended that deadline by five days, citing diplomatic progress.

Pakistan’s prime minister has offered to host US-Iran talks, which Trump said involved top officials including Vice President JD Vance.

Trump said that he had sent a plan and that it “all starts with, they cannot have a nuclear weapon.”

The New York Times, quoting unnamed officials, said that the United States had sent the 15-point plan to Iran through Pakistan.

Israel’s Channel 12 said that Trump was proposing a one-month ceasefire during which the sides would discuss a proposal that would include handing over Iran’s enriched uranium and banning further enrichment.

Read moreTrump’s supposed talks with Iran: What do we know?

Iran would also ensure safe passage through the Strait of Hormuz.

Iran in turn would see an end to all sanctions, which have been in place in various forms for years, the Israeli report said.

Iran would also receive assistance in developing civil nuclear energy at Bushehr, a key site which dates from before the 1979 Islamic revolution.

Iran on Tuesday accused Israel of carrying out a second strike on Bushehr, which lies perilously close to Gulf Arab population centers. 

“The sounds, the explosions, the missiles — they are part of our daily life now,” a 35-year-old woman in Tehran told AFP by telephone. “Our one real worry now is that our oil and gas infrastructure isn’t targeted by missile strikes.”

Iran had agreed in 2015 to broad restraints on its contested nuclear program in a deal that Trump ripped up during his first term as he joined Israel in applying pressure to the cleric-run state.

The reported new proposal would keep in place the Islamic republic which weeks earlier ruthlessly crushed mass protests, killing thousands, despite earlier vows of regime change by Trump and especially Israeli Prime Minister Benjamin Netanyahu.

Troops en route despite diplomacy 

Despite Trump’s stated hopes for diplomacy, The Wall Street Journal reported that the United States is planning to send 3,000 soldiers from the elite 82nd Airborne Division to the Middle East.

Trump’s envoys were negotiating a nuclear deal with Iran just two days before the United States and Israel launched the massive attack on February 28, killing Iran’s supreme leader Ayatollah Ali Khamanei on the first day.

Iranian missiles have found growing success penetrating Israeli defences, with AFP images showing rubble-strewn streets in the commercial hub Tel Aviv. On Tuesday, more than a dozen people were injured in Israel, including an infant, first responders said.

Israel said it conducted a “large wave” of airstrikes across several areas of Iran. Israeli military spokesman Effie Defrin said his country’s war plan was “unchanged” despite Trump’s remarks and that it would continue “to deepen the damage and remove existential threats”. 

Israel has also stepped up its campaign against the Iran-backed Hezbollah militant group in Lebanon, saying its military would take control of south Lebanon up to the Litani river, around 30 kilometres (20 miles) from the border.

Read moreTension rises between Israel and Lebanon as IDF occupies south of Litani river

Israel — which occupied southern Lebanon for nearly two decades until 2000 — carried out new strikes across the country. The Israeli military late Tuesday warned residents of Beirut’s southern suburbs, strongholds of Hezbollah, to evacuate in the face of imminent strikes.

The Israeli campaign has killed at least 1,072 people in Lebanon, with more than one million people displaced, according to authorities.

Lebanon was pulled into the Middle East war when Hezbollah began firing rockets into Israel on March 2 to avenge the killing of Khamenei.

Lebanon, whose central government has long been fragile, grew increasingly assertive by announcing it was ordering the Iranian ambassador to leave by Sunday, accusing the Islamic republic of meddling and commanding Hezbollah operations.

Bahrain, Kuwait, the United Arab Emirates and Saudi Arabia all said they had intercepted renewed drone and missile attacks as Iran kept up retaliatory strikes on US-allied Gulf states.

Oil prices, which had tumbled after Trump mooted talks on Monday, rebounded slightly in Tuesday trade, with Brent back above $100 a barrel.

(FRANCE 24 with AFP)