Fighting between the Palestinian militant group Hamas and Israel's military is escalating, claiming more than 500 lives on both sides since the group began its surprise attacks on Saturday.

The Israeli military says the attacks have killed more than 200 people and injured more than 1,000 in the country.

Hamas, which controls Gaza, said in a statement that it had to make a strategic decision to counter what it called the crimes of Israel against the Palestinian people.

An Israeli military spokesperson said hundreds of Hamas militants are believed to have crossed into Israel.

Israeli Prime Minister Benjamin Netanyahu declared that the country is at war, and ordered retaliatory strikes.

The Israeli military said on Sunday that its fighter jets had attacked three command centers of Hamas.

The militant group said it fired 100 rocket shells into a town in southern Israel as a retaliation.

Health authorities in Gaza say the Israeli attacks have killed 313 people and injured about 2,000.

The Shia militant group Hezbollah, which is based in Israel's northern neighbor Lebanon, announced on Sunday that it had fired shells into military outposts in northern Israel.

The Israel military says it responded with drone attacks on a Hezbollah position.

If Hezbollah intensifies its attacks, Israel will come under fire from the north and south. There are concerns that regional tensions will escalate.