In a new statement, Hagari says Iran has "paid the price" for its recent attacks on Israel.
He says Israel carried out "precise and targeted strikes on targets in different areas in Iran". These targets included missile manufacturing facilities, surface-to-air missile arrays and other aerial capabilities, he says.
He says Israel selected these sites from a "broad target bank", and that it would be able to "select additional targets from it and strike them if required".
"This is a clear message - those who threaten the State of Israel will pay a heavy price," he adds.Israel's military operation on Iran was still ongoing as of just before 5 am local time in Tehran, an Israeli official has confirmed to BBC's US news partner CBS.
Israel has confirmed it launched "precise strikes on military targets in Iran". It is unclear what sites were hit and the extent of the damage. The US has previously warned Israel to avoid striking nuclear and oil sites that could trigger a widening conflict in the region.
The strikes come after Iran launched nearly 200 ballistic missiles on Israel earlier this month. Israel had said it would strike back but did not detail when or what sites it might target. Iran's attack had come following Israeli strikes that killed Hamas political leader Ismail Haniyeh, Hezbollah leader Hassan Nasrallah and Iran Revolutionary Guards Corp Quds Force operations commander Brig-Gen Abbas Nilforoushan.
So far, Iranian state media has dismissed the attacks as unsuccessful, which experts tell the BBC is a typical response from Iran after such incidents. But, experts warn, that might change if reports of severe damage or deaths surfac
Blasts have also been reported in Syria, though Israel has not claimed responsibility in those attacks. Syrian air defence forces intercepted missiles and shot them down, according to Reuters and AFP news agencies, citing Syrian state media
The US was not involved in the attack, according to the Pentagon. The White House called the strikes an "exercise of self-defence". US President Joe Biden and Vice-President Kamala Harris have been briefed on the strikes and are following developments.
Bahman Kalbasi, of BBC Persian, has just shared some insight into what is happening right now in Iran.
He said that Iranian state media is currently denying these attacks caused any real damage and is saying they were unsuccessful. That has historically been a typical response from Iran when it has been the target of an attack, Kalbasi said.
"It could be a face-saving way for them to end this tit-for-tat," Kalbasi said. But that strategy could erode if there is proof showing the extent of the damage or if there are casualties, he added.
The Middle East has been on edge in anticipation of Israeli retaliation for a ballistic-missile barrage carried out by Iran on October 1, in which around 200 ballistic missiles were fired at Israel, Iran's second direct attack on Israel in six months.
"In response to months of continuous attacks from the regime in Iran against the State of Israel – right now the Israel Defense Forces is conducting precise strikes on military targets in Iran," the Israel Defense Forces said in a statement.
Israel says it has the right and duty to respond to attacks from Tehran and its proxies, which have included missile strikes launched from Iranian soil. "Our defensive and offensive capabilities are fully mobilized," it added.
Iran's state TV said several strong explosions were heard around the capital Tehran. Semi-official Iranian media said explosions were also heard in the nearby city of Karaj. Syrian state TV said explosions were also heard in the Damascus countryside and central region.
The Tasnim news agency said that "nothing has been reported about hearing the sound of rockets or airplanes in the sky of Tehran so far".
State TV cited unnamed Iranian intelligence officials as saying that the origin of the loud explosions "could be from the activation of Iran's air defense system."
Iranian authorities have repeatedly warned Israel against launching an attack, saying any strike on Iran would be met with a stronger retaliation.
The United States was notified by Israel ahead of its strikes on targets in Iran but was not involved in the operation, a U.S. official told Reuters.
"We understand that Israel is conducting targeted strikes against military targets in Iran as an exercise of self-defense and in response to Iran's ballistic missile attack against Israel on October 1st," said White House National Security Council spokesperson Sean Savett.
Washington is seeking to head off further widening of the conflict. US Secretary of State Antony Blinken said on Wednesday that Israel's retaliation should not lead to greater escalation.
Israel's defense minister said this week that enemies would "pay a heavy price" for trying to harm Israel.
