A pair of rockets fired from Gaza at Israel have killed at least two people and injured more than 40 others.

The first strike targeted a home in the eastern Gaza Strip on Thursday, the second hit a school in southern Israel, injuring four people, the Gaza Health Ministry said.

The Israeli military said the rockets were fired from within Gaza, and the rocket that hit the school was a Grad rocket, the military said.

It said there were no casualties.

In recent weeks, Israel has targeted homes, mosques, schools, markets, markets and shops belonging to Hamas, the Islamist group that rules Gaza.

Hamas has denied any involvement in any of the attacks.

The rocket fire comes as Israel is battling a surge in Palestinian suicide bombings.

A Reuters/Ipsos poll released on Thursday showed that a majority of Israelis believe that Israel is doing a good job of tackling the Palestinian militant group Hamas.

Israel has also come under fire from international bodies for the use of disproportionate force against Palestinians.

Israeli Prime Minister Benjamin Netanyahu has defended his military actions and blamed Hamas for attacks that have killed scores of Israelis in recent years.

In April, Israeli forces killed three Palestinian teenagers in a strike that hit a bus and a house in the West Bank.

The three killed were brothers, and Israeli authorities have blamed Hamas.

In the latest attack, the Israeli military targeted the home of an 18-year-old Hamas member in the Gaza Strip.

The house was hit at around 10 a.m. local time, the Israel Defense Forces said.

In a separate incident, Israeli soldiers shot and wounded a man in the southern Gaza Strip, who died at a hospital.

The army said the man was carrying an Israeli army identification and had fired several rounds.

It did not elaborate.