Israel has responded with airstrikes to a barrage of rockets from Gaza, in a deadly uptick in violence described by a senior Israeli army official on Tuesday as the most severe escalation in the coastal enclave since the 2014 war.

Palestinian militants launched nearly 400 rockets and mortar shells from the Gaza Strip into Israel, Israeli army spokesman Jonathan Conricus said, prompting attacks on more than 100 military targets in response.

Six people were killed in Gaza, the Hamas-controlled Palestinian Health Ministry said, at least four of whom were militants. One other person was killed in the Israeli town of Ashkelon in a house that was hit by a rocket.

There were injuries reported on both sides.

Israel's Iron Dome missile defence system intercepted more than 100 rockets, Conricus said.

Tanks, the air force and the navy took part, targeting facilities belonging to the Hamas movement, which controls Gaza, and Palestinian Islamic Jihad, a militant group, he added.

The violence was triggered by a botched Israeli army operation on Sunday, in which seven Palestinian militants and an Israeli officer were killed.

Missile fire from Gaza began on Monday. Among the sites hit by Israel in retaliation were munitions storage and underground infrastructure, as well as four large buildings belonging to Hamas, including the premises of the al-Aqsa broadcaster, a security facility and an intelligence service facility, Conricus said.

Hamas published footage of an anti-tank missile attack on an Israeli bus. One Israeli soldier was injured in the strike on Monday.

A Hamas spokesman threatened further attacks on Israeli targets and the group has ordered an international probe into what it claims were Israeli attacks on civilian targets.

Israel's security cabinet is meeting to discuss how to proceed on Tuesday.

According to Israeli information, Hamas has around 20,000 mortars and rockets with varying ranges in their arsenal, some of which could hit Tel Aviv or Jerusalem.

Army spokesman Conricus accused Hamas of using Gaza residents as "human shields."

"Hamas initiated the violence and is bringing destruction to the Gaza Strip," he said, adding that the group's leaders had meanwhile gone into hiding.

Hamas is considered a terrorist organization by Israel, the United States and the European Union.

Israel imposed a blockade on the Gaza coastal region over 10 years ago. The blockade is supported by Egypt, which borders the enclave to the west. Both countries cite security concerns for the blockade.

Around 2 million people live in Gaza, where clean drinking water and electricity are limited.

In response to this week's spike in violence, the German Foreign Office condemned Israeli airstrikes on the territory. "There can be no justification for this violence against innocent civilians," a spokeswoman said.