The Israeli army has intensified its offensive on the Gaza Strip, striking Hamas sites on the second day of a military operation.

The offensive has set off the heaviest fighting between Israel and the Islamic terrorist group since an eight-day battle in November 2012.

Smoke trails are seen after Hamas rockets were fired in the southern Gaza Strip towards southern Israel.

Smoke trails are seen after Hamas rockets were fired in the southern Gaza Strip towards southern Israel.

Terrorists unleashed rocket salvos deep into Israeli territory and Israel mobilised thousands of forces along the Gaza border for a possible ground invasion into the Palestinian territory.

Since the offensive began yesterday, Israel has attacked more than 400 sites in Gaza, killing at least 32 people.

The strikes from air and sea came after terrorists fired more than 160 rockets at Israel, including one that reached the northern Israeli city of Hadera for the first time. The city is about 100 kilometres (60 miles) from Gaza.

The army said it attacked more than 160 sites in Gaza early today, including 118 concealed rocket-launching sites, six Hamas compounds, 10 militant command centres, weapons storage facilities and 10 tunnels used for terrorist activity and to ferry supplies in from Egypt.

Gaza health official Ashraf Al-Kedra said the new airstrikes killed one terrorist in south Gaza, as well as an Islamic Jihad operative, his mother, and four siblings in northern Gaza. Another man was killed on a motorbike.

Four rockets were fired from Gaza towards Israel overnight, the army said, a significant decline from the large number that hit the night before, setting off air raid sirens in Jerusalem, Tel Aviv and other areas.

By early today, air raid sirens had sounded in Tel Aviv and Israel’s south and the army said two rockets were apparently intercepted above the city by an anti-missile battery.

An IDF poster aims to put the terrorist rocket bombardments in perspective.

An IDF poster aims to put the terrorist rocket bombardments in perspective.

Military spokesman Lieutenant Colonel Peter Lerner said the military’s aim was to take a “substantial toll” on Hamas and to deplete its rocket capabilities. He said the army would gradually ramp up its strikes on Gaza.

“The organisation is going to pay for its aggression. It is literally holding us hostage with its rockets,” he said. “The country is not willing for this situation to continue.”

Palestinian president Mahmoud Abbas has called on the international community and the United Nations to “provide international protection for our people”.

Speaking from the West Bank, he said in a televised statement that Hamas leaders in Gaza want to restore calm.

“I have been in contact with the regional and international parties in the last few days, particularly Hamas leaders in Gaza, and everyone I’ve talked to expressed his willingness to restore the truce and stop the escalation,” Mr Abbas said.

He called the Israeli offensive on Gaza an “orchestrated and brutal aggression”.