U.S. President Donald Trump said Monday that a proposed 45-day ceasefire with Iran was a "very significant step” but "not good enough” for him to sign, as Iranian officials wowed to keep fighting.

Talk of a ceasefire came as the U.S. and Israel struck targets across Iran, including major petrochemical facilities, while time ticked down to Trump's Tuesday deadline for Iran to reopen the Strait of Hormuz or face attacks on its civilian infrastructure.

Meanwhile Iran continued missile and drone attacks around the region.

Trump said intermediaries between the U.S. and Iran "are negotiating now" on improving the ceasefire proposal, which U.S. media reported was being mediated by Pakistan, Egypt and Türkiye.

"It's not good enough, but it's a very significant step," he told reporters at an Easter egg roll at the White House.

Trump added that he would still go through with his threat against civilian targets if a deal is not reached.

He also brushed off concerns that hitting Iran’s power facilities as he has threatened after a deadline expires this week would be a war crime.

"I’m not worried about it,” he said when asked what he would say to those who allege that striking power plants would breach the laws of war.

"You know the war crime? The war crime is allowing Iran to have a nuclear weapon," the president said.

Iran's IRNA state news agency said Tehran "has rejected a ceasefire and insists on the need for a definitive end to the conflict" in a message relayed to America via Pakistan.

Neither Trump nor IRNA named any specifics of the proposed ceasefire.

Iran's military would "continue the war as long as the political authorities see fit", army spokesman Mohammad Akraminia told the ISNA news agency.

'Living in Hell'

Trump is due to address the conflict in a press conference at 1700 GMT.

The Republican leader had given Iran until 0000 GMT Wednesday to open the Strait of Hormuz, a waterway that is crucial to global oil and gas flows, or else face strikes on bridges and power plants.

In a stark, expletive-laden social media post on Sunday, Trump demanded: "Open the Fuckin' Strait, you crazy bastards, or you'll be living in Hell."

The Revolutionary Guards, however, said Hormuz "will never return to its former status, especially for the U.S. and Israel".

Iran's virtual blockade of Hormuz has sent oil and gas prices soaring and pushed countries around the world to enact measures to contain the fallout.

Without singling out either side in the conflict, International Committee of the Red Cross chief Mirjana Spoljaric said in a statement that had already been widespread destruction of "essential" infrastructure and that "any war fought without limits is incompatible with the law" and "indefensible".

International Atomic Energy Agency (IAEA) chief Rafael Grossi warned against further strikes near Iran's Bushehr nuclear plant, saying one recent impact hit just 75 meters (245 feet) from the perimeter.

'We will reach anyone'

Earlier Monday, Israeli strikes had hit major Iranian petrochemical facilities including Assaluyeh on the Gulf coast, the country's biggest, and another outside Shiraz in central Iran.

Israel's military said it had also struck Iranian air force targets including planes and helicopters at airports in Tehran and elsewhere.

Iran's Guards posted on Telegram on Monday that their intelligence chief Majid Khademi had been killed at dawn in U.S.-Israeli strikes.

Israel's military also said it had killed Asghar Bagheri, commander of the Guards' Quds Force special operations unit, on Sunday.

"We will reach anyone who seeks to harm us," Israeli Prime Minister Benjamin Netanyahu said.

The Guards' Intelligence Organization vowed a "major retaliatory strike" against those responsible for killing their commanders, their official Sepah news website reported.

Yemen's Houthi rebels said they launched an attack targeting Israel, supporting their backer Iran and Lebanon's Hezbollah.

Oil squeeze

The war, which erupted on Feb. 28 with U.S.-Israeli strikes on Iran that killed supreme leader Ayatollah Ali Khamenei, has engulfed the Middle East and roiled the global economy.

The worldwide oil squeeze has hit aviation, with Indonesia on Monday saying it would increase a jet fuel surcharge and low-cost carrier Air Asia X announcing ticket price hikes of up to 40%.

South Korea will send ships to fetch oil from Saudi Arabia's Red Sea port of Yanbu, avoiding Hormuz altogether, a ruling party MP said, while Taiwan's government said it too would take the Red Sea route.

Gulf nations allied with the U.S. have also been sucked into the war, with Kuwait and the UAE reporting strikes and injuries from Sunday to Monday.

Iran has continued to launch attacks at Israel, where the military and medics said four bodies were recovered from a residential building in the northern city of Haifa that was struck by a missile.

Iranian media reported several attacks on residential areas of Tehran, while the state broadcaster said gas outages hit parts of the capital after a strike on a university.

On another front, Lebanon has increasingly been dragged into the war since the Iran-backed armed group Hezbollah targeted Israel on March 2.

Israel has struck back and invaded parts of southern Lebanon, with army chief Lieutenant General Eyal Zamir visiting troops there Sunday and pledging to intensify strikes.

AFP journalists saw a large plume of smoke rising over Beirut's southern suburbs on Monday after an Israeli strike that the army said targeted Hezbollah.

Israel's military said it was reviewing the incident after "reports of casualties among Lebanese civilians not involved in the fighting".

Lebanon's health ministry said an Israeli attack killed a paramedic from the Hezbollah-allied Risala Scouts association on Monday.

Hezbollah announced attacks on Israeli targets in south Lebanon and across the border, including launching a missile and attack drones at a base near the central city of Hadera.