Iran warned on Saturday it would defend itself after Israeli air strikes killed at least two soldiers and further stoked fears of a full-scale regional war in the Middle East.

Israel warned Iran would "pay a heavy price" if it responded to the strikes, and the United States, Germany and Britain demanded Tehran not escalate the conflict further.

US President Joe Biden said he hoped "this is the end" after the pre-dawn Israeli strikes, noting that "it looks like they didn't hit anything other than military targets."

The European Union called for all parties to exercise utmost restraint to avoid an "uncontrollable escalation."

Other countries, including many of Iran's neighbours, condemned Israel's strikes and some, such as Russia, urged both sides to show restraint and avoid what Moscow dubbed a "catastrophic scenario."

Iran insisted it had the "right and the duty" to defend itself, while its Lebanese ally Hizbollah said it had already launched rocket salvos targeting five residential areas in northern Israel.

The Israeli army said 80 projectiles were fired across the border on Saturday.

Hizbollah later issued evacuation warnings for more than a dozen named locations in Israel, in a new move mirroring the warnings long put out by the Israeli military for areas of Gaza and Lebanon where it intends to operate.

Confirming its own strikes after explosions and anti-aircraft fire echoed around Tehran, the Israeli military said it had hit Iranian missile factories and military facilities in several regions.

The "retaliatory strike has been completed and the mission was fulfilled", and Israeli aircraft "returned safely", a military spokesman said.

Iran confirmed Israel had targeted military sites around the capital and in other parts of the country, saying the raids caused "limited damage" but killed four soldiers.

Iran's armed forces general staff said only radar systems were damaged in the strikes and held back from any threat of immediate retaliation.

"While reserving its legal and legitimate right to respond at the appropriate moment, Iran is prioritising the establishment of a lasting ceasefire in Gaza and Lebanon," it said.

Foreign Minister Abbas Araghchi said there were "no limits" to Iran's determination to defend itself.

Israel had vowed to retaliate after Oct 1, when Iran fired around 200 missiles in only the second ever direct attack against its arch-foe. Most of those missiles were intercepted but one person was killed.

The Israeli retaliation drew condemnation from Iraq, Pakistan, Syria and Saudi Arabia, which warned against further escalation. Jordan said Israeli jets had not used its airspace. Turkey was one of the most outspoken critics, calling for an end to "terror created by Israel."

Israel is already engaged in combat on two fronts.

Since last month, it has been fighting a war against Hizbollah in Lebanon, including strikes that have killed the group's senior leadership and ground incursions seeking to destroy missile sites.

And, for more than a year since Hamas' Oct 7, 2023 attack, Israel has been fighting a war in Gaza that has caused mass civilian casualties in the densely populated Palestinian territory.

The United Nations has warned the "darkest moment" of that conflict was unfolding, with Palestinians facing a dire humanitarian crisis and daily Israeli bombing.

A defence official said there was "no US involvement" in the strikes on Iran, but afterwards Israeli President Isaac Herzog paid tribute to "our great friend the USA for being a true ally, and for the overt and covert cooperation." He did not elaborate.

US National Security Council spokesman Sean Savett said Israel's response to Iran was "an exercise in self-defence."

He urged Iran to "cease its attacks on Israel so that this cycle of fighting can end without further escalation."

The Israeli military has blamed "Iran and its proxies" in the region for "relentlessly attacking Israel since Oct 7", when Hamas attacked Israel, triggering the Gaza war.

That attack resulted in the deaths of 1,206 people, mostly civilians, according to an AFP tally of official Israeli figures.

Dozens of hostages seized on that day are still held by militants in Gaza.

Israel's retaliatory bombardment and ground war in Gaza has killed 42,924 people, the majority civilians, according to data from the Hamas-run territory's health ministry, figures the United Nations considers reliable.

In late September, Israel turned its focus to Lebanon hitting, Hizbollah targets and leaders and then sending in ground troops.

Israel says the aim is to make the north of its country safe for tens of thousands of displaced civilians to return.

At least 1,615 people have been killed in Lebanon since Sept 23, according to an AFP tally of Lebanese health ministry figures.

In April, in its first-ever direct assault against Israeli territory, Iran launched more than 300 drones and missiles.

Tehran said the barrage was retaliation for a strike on Iran's consular annexe in Damascus that killed members of its Islamic Revolutionary Guard Corps.

Explosions later in April shook Iran's Isfahan province in what US officials, cited by American media, said was Israeli retaliation.

Iran said its Oct 1 missile attack on Israel was retaliation for an Israeli air raid that killed Hizbollah chief Hassan Nasrallah as well as the assassination in Tehran of Hamas political leader Ismail Haniyeh.

On Friday, Gaza's health ministry accused Israeli forces of storming the last functioning hospital in the territory's north in a raid it said left two children dead.

The Israeli military said its forces were operating around Kamal Adwan Hospital in north Gaza's Jabalia refugee camp but it was "not aware of live fire and strikes in the area of the hospital."

The Israeli military says it is seeking to destroy operational capabilities Hamas is trying to rebuild in the north.

Also on Friday, Gaza's civil defence agency said Israeli drone strikes killed 12 people waiting to receive aid near the Al-Shati refugee camp.