Hamas on Saturday denounced as "barbaric" overnight strikes it said damaged a Gaza children's hospital, while the Israel army said it was responding to rocket fire from the enclave.

The Israel army said it struck three Hamas targets, including a rocket manufacturing site, underground infrastructure and a military post, after two rockets were fired from the Gaza Strip.

But Gaza's ruling Hamas in a statement said a "barbaric" Israeli strike had damaged a children's hospital and a centre for people with special needs.

Medical sources in Gaza said the strikes "lightly wounded" two civilians, including a child.

"Hamas will bear the consequences for all terror emanating from Gaza," the Israeli army said in a tweet.

Sirens had sounded on Friday night in the southern port city of Ashkelon and the area surrounding the Gaza Strip, according to an army statement.

"Two rockets were fired from the Gaza Strip towards Israeli territory," the army statement said, adding that they were intercepted by the Iron Dome Aerial Defence System.

There were no reports of damage as a result of the interceptions. 

Israeli emergency medical services said several people were treated for shock.

The latest fire from the Palestinian enclave came over a month after one rocket was fired from the coastal strip into Israel.

Islamist group Hamas, which Israel considers a terrorist organisation, seized control of Gaza from rival Palestinian movement Fatah in 2007 in a near civil war.

Since then Hamas has fought three devastating wars with Israel in the coastal territory, where about two million Palestinians live.

Israel has since maintained a crippling blockade on the Gaza Strip to prevent Hamas from arming.