The statement seemingly retracted earlier threats to desalination plants in the region, which are crucial for providing drinking water in Gulf countries.
"The lying ... US President has claimed that the Revolutionary Guards intends to attack the water desalination plants and cause hardship to the people of the countries in the region," said the statement shared on state media on Monday.
"We are determined to respond to any threat at the same level as it creates in terms of deterrence ... If you hit electricity, we hit electricity."
On Saturday, Trump warned that Iranian power plants would be destroyed if Tehran failed to "fully open" the Strait of Hormuz to all shipping within 48 hours. Trump set a Monday deadline of 7.45pm EDT (10.45am on Tuesday AEDT).
Iranian attacks have effectively closed the Strait of Hormuz, which carries a fifth of global oil and liquefied natural gas, causing the worst oil crisis since the 1970s.
More than 2000 people have been killed during the war the US and Israel launched on February 28, which has upended markets, spiked fuel costs, fuelled global inflation fears and convulsed the postwar Western alliance.
The threat of strikes on Gulf electricity grids on Sunday raised the fear of mass disruption to desalination for drinking water, and further unsettled oil markets.
After more than three weeks of heavy US and Israeli bombardment that officials say has sharply reduced Iran's missile capabilities, Tehran has continued to demonstrate its ability to strike back.
Air raid sirens sounded across parts of northern and central Israel, including in Tel Aviv, and the occupied West Bank overnight on Sunday, warning of incoming missiles from Iran.
The Israeli military said it had begun a wide-scale wave of strikes targeting Iranian infrastructure in Tehran.
The Washington Post reported that Iran's Supreme Leader Mojtaba Khamenei was "injured, isolated, and not responding to messages directed to him".
Earlier in March, an Iranian official said the country's new supreme leader had been lightly injured.
Khamenei succeeded his father Ayatollah Ali Khamenei, who was killed in the first wave of strikes on February 28.
He has not been seen in public since his elevation.
Iranian news agencies said six people were killed and 43 injured in strikes on residential buildings in the western Khorramabad city.
Elsewhere in the region, the Saudi defence ministry said early Monday two ballistic missiles had been launched towards Riyadh.
One missile was intercepted while the other fell in an uninhabited area.
Trump's warning to strike Iran's power network came less than a day after he signalled the United States might be considering winding down the conflict, even as US Marines and heavy landing craft were heading to the region.
While attacks on electricity could hurt Iran, they could be catastrophic for its Gulf neighbours, which consume about five times as much power per capita, in part by powering desalination plants that produce most of the water consumed there.
Iran's powerful Revolutionary Guards said it would also mean the Strait of Hormuz would remain shut.
"The Strait of Hormuz will be completely closed and will not be opened until our destroyed power plants are rebuilt," the Guards said.
Iranian media on Sunday quoted the country's representative to the International Maritime Organisation as saying the strait remained open to all shipping except vessels linked to "Iran's enemies".
Only a few ships, including Indian-flagged and a Pakistani oil tanker, have reportedly been allowed safe passage.
