Air raid sirens sounded across Israel from the early hours of Sunday morning, warning of incoming missiles from Iran, after scores of people were hurt overnight in two separate attacks in the southern Israeli towns of Arad and Dimona.
The Israeli military said on Sunday it was striking Tehran just hours after Iran's attacks on southern Israel.
Trump on Saturday threatened to "obliterate" Iran's power plants if Tehran did not fully reopen the Strait of Hormuz within 48 hours, a significant escalation barely a day after he talked about "winding down" the war, now in its fourth week.
Iran warned on Sunday it would target US infrastructure, including energy facilities in the Gulf, if Trump carried out his threat, which he made as US Marines and heavy landing craft continued to head to the region.
More than 2000 people have been killed during the war the US and Israel launched on February 28.
The conflict has upended markets, spiked fuel costs, fuelled global inflation fears and convulsed the postwar Western alliance.
"President Trump's threat has now placed a 48-hour ticking time bomb of elevated uncertainty over markets," IG market analyst Tony Sycamore said.
"If the ultimatum is not walked back, we will likely see a Black Monday reopening of global equity markets in free fall and oil prices spiking significantly higher."
Tehran would likely target Gulf energy facilities in Saudi Arabia, the United Arab Emirates and Qatar, which "would deepen and prolong the pain of higher energy prices and drag the conflict into a broader regional crisis", Sycamore said.
Oil prices jumped on Friday and settled at their highest in almost four years after Iraq declared force majeure on all oilfields developed by foreign firms, Israel attacked a major gas field in Iran and Tehran responded with strikes on neighbours Saudi Arabia, Qatar and Kuwait.
Iranian attacks have effectively closed the Strait of Hormuz, a narrow choke point that carries around one-fifth of global oil and liquefied natural gas supplies, causing the worst oil crisis since the 1970s.
"If Iran doesn't FULLY OPEN, WITHOUT THREAT, the Strait of Hormuz, within 48 HOURS from this exact point in time, the United States of America will hit and oblitreate their various POWER PLANTS, STARTING WITH THE BIGGEST ONE FIRST!" Trump posted on social media around 7:45 p.m. EDT (2345 GMT) on Saturday.
The Strait of Hormuz remains open to all shipping except vessels linked to "Iran's enemies", Iran's representative to the UN maritime agency Ali Mousavi was quoted as saying in Iranian media reports published on Sunday.
His comments came from an interview published on Friday by Chinese news agency Xinhua, before Trump's threat to target Iranian power plants if the strait was not "fully open" within 48 hours.
Mousavi said passage through the waterway was possible by co-ordinating security and safety arrangements with Tehran.
Ship-tracking data has shown vessels including Indian-flagged ships and a Pakistani oil tanker have negotiated safe passage through the strait.
Iran's Khatam al-Anbiya military command headquarters said if the US attacked Iran's fuel and energy infrastructure, Iran would target all US energy, information technology and desalination infrastructure in the region.
Striking major plants could trigger blackouts, crippling everything from pumps and refineries to export terminals and military command centres.
Tehran fired long-range missiles for the first time on Saturday, while an Iranian strike landed near Israel's secretive nuclear reactor about 13km southeast of Dimona.
Iran launched two ballistic missiles with a range of 4000km at the US-British military base at Diego Garcia in the Indian Ocean, Israeli military chief Eyal Zamir said.
In southern Lebanon, Israel said its military raided Hezbollah sites on Sunday and killed 10 of the group's fighters.
Hezbollah said it attacked several border areas in northern Israel.
One person was killed in an Israeli kibbutz, emergency services said, the first fatality in Israel killed by fire from Lebanon since March 2, when Hezbollah entered the war in response to the killing of Iran's Supreme Leader Ali Khamenei.
Israel said it had instructed the military to accelerate the demolition of Lebanese homes in "frontline villages" to end threats to Israeli communities, and to immediately destroy all bridges over Lebanon's Litani river.
Trump has accused NATO allies of cowardice over their reluctance to help open the Strait of Hormuz, with most reluctant to join a war he started without consulting them.