Israel unleashed a new wave of attacks against Iran on Monday, targeting missile sites after Tehran carried out deadly overnight strikes and both sides threatened more devastation.

After decades of enmity, Israel's surprise assault on Iran last week has touched off the most intense fighting yet and triggered fears of a lengthy conflict that could engulf the Middle East.

Israel says its attacks have hit military and nuclear facilities, and killed many top commanders and atomic scientists – but a senior US official said on Sunday that US President Donald Trump told Israel to back down from a plan to kill supreme leader Ayatollah Ali Khamenei.

Residential areas in both countries have suffered deadly strikes since the hostilities broke out, with Israeli Prime Minister Benjamin Netanyahu slamming Iran on Sunday for allegedly targeting civilians.

"Iran will pay a very heavy price for the premeditated murder of civilians, women and children," he said, during a visit to the site of a missile strike on a residential building in the coastal city of Bat Yam, near Tel Aviv.

His remarks came hours after Iranian missile fire killed at least 10 people, according to authorities, pushing the death toll in Israel up to 13 since Iran began its retaliatory strikes on Friday.

Iranian state television reported at least five people were killed on Sunday by an Israeli strike that hit a residential building in downtown Iran.

Colonel Reza Sayyad, a spokesman for Iran's armed forces, threatened a "devastating response" to Israel's attacks.

"Leave the occupied territories (Israel) because they will certainly no longer be habitable in the future," he warned in a televised address, adding shelters will "not guarantee security".

Iran's health ministry reported at least 224 people killed and more than 1,200 wounded in Israeli attacks since Friday. Israel has claimed strikes as far away as Mashhad in Iran's far east, 2,300 km from Israel.

The Israeli military said early Monday that it was striking surface-to-surface missile sites in central Iran, adding it was "operating against this threat in our skies and in Iranian skies". (AFP)