Palestinians check an impact crater at the site of an Israeli air strike in Gaza Strip. (AFP)

Israel carried out air strikes against the Gaza Strip overnight in response to a rocket fired from the Hamas-controlled Palestinian enclave, the army said Thursday.

Prime Minister Benjamin Netanyahu was at campaign event in Ashkelon north of Gaza on Wednesday evening when what the army called a "projectile" was fired from the strip, setting off warning sirens.

The army said the "projectile was fired from the Gaza Strip towards Israeli territory and was intercepted by the Iron Dome defence system".

In response, it said, "planes and helicopters hit several Hamas terrorist targets in the Gaza Strip. Military posts were among the targets."

No injuries were reported on either side, though a security source in Gaza said damage was reported at a number of Hamas sites.

Israel's public broadcaster KAN 11 showed images of a security guard informing Netanyahu, who is campaigning for re-election as head of his Likud party, of a "red alert" late Wednesday.

The prime minister waved goodbye before being hustled from the room with his wife Sarah.

On September 10, the head of the Likud party had also been evacuated from an election rally, in the southern city of Ashdod, after sirens warned of an attack from Gaza.

On Thursday, the embattled premier was facing off against longtime rival Gideon Saar in a Likud leadership contest that could threaten his grip on power.

Last week, two rocket attacks were launched against Israel from Gaza without causing injury, Israel's army said.

In response, Israel twice bombed Hamas installations in the enclave.

Israel holds the Islamist movement responsible for all rocket attacks coming from Gaza, though the Jewish state also targets other armed groups operating there.

Since 2008, Israel has fought three wars with Hamas and its allies in Gaza, where two million Palestinians live amid violence, poverty and a 12-year Israeli blockade.