Avenging the October 1 attack, Israel struck back at Iran conducting "precise strikes" on military facilities in Tehran and nearby provinces on Saturday, media reports said.

Over 100 Israeli fighter jets including the F-35 stealth fighters flew over Tehran and completed the mission before dawn.

The fighter jets flew for 1,000 kilometres and struck the radar and air defence systems of Iran before hitting military sites including a missile manufacturing unit.

Taking responsibility for the attack, Israel said it conducted "precise strikes" on Tehran.

Meanwhile, Iran initially claimed that the explosions across the capital Tehran were due to the activation of air defence systems, but later admitted that the strikes caused "limited damage" to military sites, according to reports.

Two Iranian soldiers were killed in the attack.

"We are prepared to respond to any Israeli 'aggression'," Iran's semi-official Tasnim news agency reported, citing sources in the government.

"There is no doubt that Israel will face a proportional reaction for any action it takes," they added.

The Israeli army has warned Iran of paying a "heavy price" if it begins a new round of escalation.

The US has termed Israel's attack an "exercise of self-defence" and urged Tehran to avoid any further escalation.

"The US was informed by Israel beforehand about the attacks and there is no involvement of Washington in the strikes," AFP reported quoting sources in the US government.

The airspace in three countries was under a temporary lockdown after the strikes. Iran, Iraq and Syria shut the airspace in response to the strike to preserve the safety of civil aviation.