U.S. President Donald Trump said Tuesday he sent a peace plan to Iran and voiced optimism about ending nearly a month of war, as Tehran signaled it would allow “non-hostile” vessels through the vital Strait of Hormuz.

The diplomatic hints came amid continued violence. An Iranian missile wounded people in Israel, while Israel expanded strikes and said it aims to control a strip of southern Lebanon.

Trump, whose recent statements have swung between threats and de-escalation, said the United States was “in negotiations right now” with Iran, though Tehran has not confirmed 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 elaborate but said it related to the Strait of Hormuz, a chokepoint for about one-fifth of global oil.

Shortly after, Iran told the International Maritime Organization it would permit safe passage for “non-hostile vessels.” Shipping had already slowed as insurers pulled back.

Possible nuclear framework

Trump had earlier threatened to “obliterate” Iran’s power plants if the strait remained blocked, then extended a deadline citing progress. Pakistan’s prime minister offered to host talks involving senior U.S. officials, including Vice President JD Vance.

Trump said his proposal “all starts with, they cannot have a nuclear weapon.”

The New York Times reported a 15-point plan was sent via Pakistan. Israel’s Channel 12 said it includes a one-month ceasefire, talks on handing over enriched uranium, a halt to further enrichment, sanctions relief and guarantees on maritime access.

The plan also envisions assistance for civilian nuclear energy at Bushehr. Iran on Tuesday accused Israel of striking the site again.

“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 agreed in 2015 to limits on its nuclear program, a deal Trump later withdrew from during his first term.

Fighting continues

Despite diplomatic signals, The Wall Street Journal reported the U.S. plans to deploy 3,000 troops from the 82nd Airborne Division to the region.

Iranian missiles have increasingly penetrated Israeli defenses, with more than a dozen people injured Tuesday. Israel said it carried out a “large wave” of airstrikes across Iran and would continue operations to remove threats.

Israel has also intensified strikes against Hezbollah in Lebanon, saying it will control territory up to the Litani River. Airstrikes and evacuation warnings hit Beirut’s southern suburbs.

Lebanese authorities say more than 1,000 people have been killed and over a million displaced.

Hezbollah began firing rockets into Israel on March 2 after the killing of Iran’s supreme leader Ali Khamenei. Lebanon later ordered the Iranian ambassador to leave, accusing Tehran of interference.

Gulf states including Bahrain, Kuwait, the United Arab Emirates and Saudi Arabia reported intercepting Iranian drones and missiles.

Oil prices, which fell on talk of negotiations, edged back up Tuesday, with Brent crude topping $100 a barrel.