In the latest tit-for-tat violence ahead of a March 2 general election in the Jewish state, the Israeli Air Force targeted "Islamic Jihad terror sites" throughout Gaza and near the Syrian capital Damascus, a military statement said.

It followed more than 20 rockets and mortars fired from the Palestinian enclave, themselves a response to the killing of an Islamic Jihad militant along the Gaza-Israel border.

Islamic Jihad, which along with allied group Hamas has fought three wars with Israel since 2008, operates in both the Gaza Strip and Syria.

The Israeli army said it had struck Islamic Jihad targets on the outskirts of Damascus, including a base "used as a hub" for the group's activities in the country.

Islamic Jihad, which is allied with Syrian President Bashar al-Assad, confirmed early Monday that two of its fighters were killed.

The Syrian Observatory for Human Rights, a Britain-based war monitor, later confirmed that four additional pro-Assad, Iran-backed fighters died in the strike.

At least one of the Iran-backed fighters was Syrian, while the nationalities of the others remained unknown, Observatory head Rami Abdel Rahman told AFP.

Since the start of the Syrian conflict in 2011, Israel has carried out hundreds of strikes in Syria, mainly targeting government troops as well as allied Iranian forces and fighters from the Lebanese group Hezbollah.

It is rare for them to claim such strikes directly.

- Bulldozed -

Earlier on Sunday, Israel's military said it had killed a militant in Gaza who had tried to plant an explosive device near the border fence.

Israel later confirmed that it extracted the militant's body with a bulldozer.

Israel's hawkish Defence Minister Naftali Bennett has pursued a policy of retaining the bodies of militants from Gaza as bargaining chips to pressure Hamas, which has held the bodies of two Israeli soldiers since 2014.

A video emerged later on social media, which was authenticated by AFP, showing a bulldozer approaching a body while a group of young, apparently unarmed men, were trying to retrieve it.

The sound of gunfire is heard and the men ultimately run away as the bulldozer scoops up the body.

Hours later, more than 20 rockets and mortars were launched from Gaza towards Israel, setting off warning sirens in the southern city of Ashkelon and several other locations.

More than a dozen were intercepted by the Jewish state's Iron Dome missile defence system, the Israeli army said, adding there were no reports of serious injuries in Israel.

Islamic Jihad claimed responsibility for the rockets, calling them a response to the killing of one its fighters along the Gaza border early Sunday.

Israeli military said it responded to the rocket fire by targeting "dozens" of Islamic Jihad targets throughout Gaza.

Health officials in Gaza said four people were wounded.

Hamas and Israel last fought a full-scale war in 2014, but smaller flareups are relatively common.

In November, Islamic Jihad and Israel fought a three-day conflict that left 35 Palestinians dead and more than 100 wounded, according to official figures.

Under the informal agreements in the past year, Israel has slightly eased a blockade of the impoverished Palestinian enclave in exchange for relative calm.

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