Hamas has said it will expand its rocket fire to directly hit the Israeli towns of Beersheba and Ashdod, some 30 kilometres north and west of Gaza, if air strikes on the enclave continue, as the Israeli army warned that overnight attacks on Israel were "the most intense" since the last conflict in 2014.

At least seven people have been killed since heavy cross-border fire erupted Monday afternoon, sparking fears of a new war.

Local medical officials recorded six fatalities in Gaza, five of them militants. In Israel, one civilian was killed in the southern Israeli town of Ashkelon. Local media reported he was a West Bank Palestinian from Hebron although his identity has yet to be confirmed.

In total, Gaza militants have fired at least 400 rockets and mortars into Israel whose officials said Tuesday they had struck more than 100 targets in Gaza, including Hamas's Al-Aqsa TV headquarters and several Hamas security buildings.

The spokesman for the Hamas military wing said in a Monday statement that Ashkelon, just over 10 km north of Gaza, "has entered the range of fire as a response to the bombing of buildings in Gaza."

He added that Ashdod and Beersheba, 30km away, "are the next targets if the enemy continues bombing civilian buildings."

Jonathan Conricus,an Israeli army spokesman, said it was "too early" to say whether war would break out but warned that Gaza militants had in excess of 20,000 rockets and mortars within their arsenal and so the army was prepared for the long haul.

“Hamas is forcing this violence and really bringing destruction upon the Gaza Strip because of its actions. We hold Hamas responsible," he said.

He added that the Israeli army had "enhanced troops” in the south of the country but not yet mobilised reserves.

The sudden flare up in fighting was triggered by a botched Israeli special forces raid on southern Gaza on Sunday night.

Seven Palestinians, including a local Hamas commander, and a high ranking Israeli officer, were killed when the Israeli covert patrol encountered Palestinian fighters at a checkpoint three kilometres into Gaza in the eastern areas of Khan Younis.

Hamas officials told The Independent they believed the raid to be a “top-level” intelligence-gathering operation that had gone wrong. The Israeli army declined to comment.

Israeli identified its slain officer as Lieutenant-Colonel “M”, a 41-year-old father-of-two from north Israel. He was the most senior ranking officer to be killed in the enclave since the 2014 war.

Shortly after funerals, Gaza militants launched a barrage of rocket fire which continued into Tuesday morning.

Israel has responded with dozens of air, tank and naval strikes on Gaza targeting what they have identified as military infrastructure and a television building.

A ball of fire above the building housing the Hamas-run television station al-Aqsa TV in the Gaza Strip during an Israeli air strike on 12 November (AFP)

The wave of violence has threatened to derail a long-term ceasefire agreement brokered by Egypt that had seen significant progress over the last few weeks.

Just hours before Sunday's disastrous raid, the Israeli prime minister Benjamin Netanyahu had given a lengthy speech in Paris defending Israeli’s decision to allow Qatar to deliver $15 million to Hamas to pay salaries. In exchange, Hamas scaled back its weekly demonstrations along the Israeli border.

The UN and Egypt have scrambled to pull back both sides from the brink of war this summer following eight months of clashes along the border fence with Israel.

Since March, tens of thousands of Gaza residents have marched towards Israel every Friday demanding the right to return to their ancestral lands, which they were forced from or fled during the 1948 conflict which surrounded the creation of Israel. They have also protested against an 11-year-old crippling Israeli siege on the Strip.

More than 218 Palestinians have been killed by Israeli fire since then.

Facing mounting criticism, Israel defended its actions saying that protesters have launched burning kites and balloons tied with explosives at Israel and attempted to break the border fences.