The Israeli military said on Saturday it was carrying out "precise strikes" on military targets in Iran.

"In response to months of continuous attacks from the regime in Iran against the State of Israel –- right now the Israel Defense Forces (Israeli military) is conducting precise strikes on military targets in Iran," the military said in a statement.

"Our defensive and offensive capabilities are fully mobilised," the military said in a statement. Military spokesman Rear Admiral Daniel Hagari, in a separate statement, called on the people to be "alert and vigilant".

Iranian state TV said "strong explosions" were heard around the capital Tehran, without specifying the cause of the blasts. "Minutes ago, the sound of strong explosions was heard from around Tehran, the source of these sounds is not yet clear," a state TV presenter said.

An AFP reporter also heard the explosions.

Several Tehran residents reported hearing "strong and loud sounds" around the capital, the official IRNA news agency said.

The blasts were first heard around 2:15 am local time, mainly to the west of the city, it said.

Israel has vowed to respond to Iran's missile attack on October 1.

Israeli strikes on military targets in Iran are "an exercise of self-defense" following Tehran's ballistic missile attack earlier this month, the National Security Council spokesman Sean Savett said.

On the other hand, Syrian air defences intercepted "hostile targets" near Damascus early Saturday, state news agency SANA reported, as Israel said it was launching strikes in Iran.

"Our anti-aircraft defense is confronting hostile targets in the skies around Damascus," SANA said on Telegram after reporting "sounds of explosions" in the vicinity of the Syrian capital.

Iran's state TV said Saturday that operations at Tehran's airports including Imam Khomeini International Airport were "normal" after it reported several explosions around the capital.

"Operations at Imam Khomeini International Airport and Mehrabad Airport are normal and they continue to operate according to the schedule," the state TV presenter said, citing the chiefs of Mehrabad and Imam Khomeini airports.

Iranian media said Saturday there were no fires or explosions reported at a key Tehran refinery.

"There are no reports of fire or explosions at a Tehran refinery," Tasnim news agency reported, referring to a key oil refinery south of the capital.