At least two Grad rockets launched by Gaza militants hit Israel's southern city of Beersheba early Sunday morning, no injury or damage reported.

People in the Negev desert's largest city with some 150,000 residents, about 40 km east of Gaza, reported hearing the blasts as the rockets struck.

"And another one now," resident Ehud Zion Waldoks said right after the second explosion. "I had to go back to sleep. I was awaken from sleep and running downstairs (to an apartment bomb shelter)."

City officials closed schools after the strike, as Sunday is the beginning of the Israeli work week.

Two Kassam rockets also hit areas closer to Gaza, according to The Jerusalem Post.

Israeli Air Force aircraft targeted a rocket launch site during the night and its firing crew in Central Gaza, the army told Xinhua.

Military sources said a Hamas militant was killed in the strike, according to Israel Radio.

Palestinian militants in the coastal enclave fired over 610 rockets into Israel in 2012, with over 150 launched in October.

The army said that it holds Hamas exclusively responsible for any violence emanating out of Gaza.