Militants in Gaza fired more rockets at Tel Aviv on Wednesday, targeting Israel's heartland after Israeli attacks in the enclave that Palestinian officials said have killed at least 38 people.

No casualties were reported in the rocket barrages, on the second day of an intensified Israeli offensive in the Hamas-dominated Gaza Strip. Missiles from Israel's Iron Dome defence system shot into the sky to intercept the projectiles.

The rocket salvoes have sent people racing for bomb shelters, but businesses remained open in Israel, traffic flowed and the Tel Aviv Stock Exchange seemed to be unfazed, with shares opening higher.

In the Gaza Strip, residents were shaken overnight by the sound, every few minutes, of powerful explosions that sent up plumes of smoke.

At least 18 civilians, including five children, were among the 27 Palestinian dead since Israel stepped up its assault on Tuesday, and 150 people have been wounded, hospital officials said.

Israeli leaders, who seem to have wide popular support at home for the Gaza operation, have warned of a lengthy campaign and possible ground invasion of the heavily populated Palestinian territory. But questions were already been asked on radio talk shows about an exit strategy and when rocket fire would end.

At a sidewalk cafe on a fashionable avenue in Tel Aviv, Israel's most free-wheeling city and its commercial capital, patrons seemed to take Tuesday's air raid siren in stride, staying in line for their coffee as joggers and cyclists passed.

Gaza's busiest shopping street was largely deserted on Wednesday, although some convenience stores remained open.

"I am fine, as long as Tel Aviv is being hit, I am fine," said Abu Ahmed, 65, as he bought cigarettes.

The Israeli military said that overnight it attacked 118 concealed rocket launching sites, weapons storage facilities, 10 tunnels and 10 command and control positions.

In an emerging pattern, it was also going after commanders in Gaza's militant groups - in attacks which Palestinian officials said caused casualties among the men's families.

In an air strike on a home in northern Gaza on Wednesday, a top leader of the Islamic Jihad group and five of his family members were killed, the Palestinian Interior Ministry said. An 80-year-old Palestinian woman was killed in an Israeli attack on another target in central Gaza, local officials said.

The build-up to the most serious hostilities between Israel and Gaza militants since an eight-day war in 2012 began three weeks ago with rocket attacks following the abduction and killing of three Jewish seminary students in the occupied West Bank.

Egypt brokered a truce in the conflict two years ago, but its military-backed government is hostile toward Islamist Hamas and there were no immediate signs of intervention to halt the current fighting between the group and Israel's powerful armed forces.

Israeli leaders have called the persistent Palestinian rocket salvoes - which have also triggered air raid sirens in Jerusalem - intolerable and have approved the potential mobilisation of up to 40,000 reserve troops.

"The government has instructed the military to deploy forces along the border with Gaza to be ready for any contingency," said Mark Regev, a spokesman for Prime Minister Benjamin Netanyahu. "We have a number of options. Our goal, our overriding goal, is to safeguard the people of Israel and to end the launching of rockets from Gaza on our citizens."

An Israeli military spokesman said militants in Gaza have dozens of long-range rockets. One of them, an M-302 projectile, hit the coastal city of Hadera, some 97 km north of the Gaza Strip on Tuesday, landing near a house but causing no injuries, the military said.

In a bold infiltration on Tuesday, gunmen from Hamas landed on the shore near Zikim adjacent to the Gaza border, where a kibbutz and a military base are located. Four gunmen were killed.

Washington backed Israel's actions in Gaza while the European Union and United Nations urged restraint on both sides.

"We strongly condemn the continuing rocket fire inside of Israel and the deliberate targeting of civilians by terrorist organisations in Gaza," White House spokesman Josh Earnest said.

"No country can accept rocket fire aimed at civilians and we support Israel's right to defend itself against these vicious attacks."

Western-backed Palestinian President Mahmoud Abbas, who is based in the Israeli-occupied West Bank and entered a power-share with Hamas in April after years of feuding, said he had spoken to Egypt about the Gaza crisis.

Under President Abdel Fattah al-Sisi, Cairo has secured closures on the Egyptian-Gaza border, increasing economic pressure on Hamas from a long-running Israeli blockade.

"Sisi stressed Egypt was interested in the safety of the Palestinian people in the Gaza Strip and sparing this grave assault," a statement from Abbas's office said, adding that Cairo would "exert efforts to reach an immediate ceasefire".

In the West Bank, about 400 Palestinian youths, chanting their support for Hamas's armed wing, threw stones at an Israeli army checkpoint on Wednesday. Soldiers responded with tear gas and rubber bullets.

Israel has blamed Hamas for the killing of the three Jewish seminary students who disappeared while hitchhiking in the West Bank on June 12. Hamas has neither confirmed nor denied a role.

The rocket fire from Gaza began after Israel arrested hundreds of Hamas activists in a West Bank sweep it mounted in tandem with a search for the youths, who were found dead last week. A Palestinian teen was abducted and killed in Jerusalem last Wednesday in a suspected revenge murder. Six Israelis have been arrested in that case.

While threatening an "earthquake" of escalation against Israel, Hamas said it could restore calm if Israel halted the Gaza offensive, once again committed to a 2012 ceasefire truce and freed the prisoners it detained in the West Bank last month.-Reuters