By Nidal al-Mughrabi and Maayan Lubell
GAZA/JERUSALEM (Reuters) -Israel hit Islamic Jihad targets in Gaza for a second day on Wednesday and Palestinian militants launched hundreds of rockets across the border, setting off sirens as far away as Tel Aviv, while Egypt began efforts to mediate an end to the fighting.
The second round of cross-border fire in a week came after Israel launched strikes on Tuesday against three Islamic Jihad commanders it said had planned attacks against Israelis, following months of escalating violence.
Cairo, which has mediated in previous rounds of fighting, had begun brokering a ceasefire, Islamic Jihad spokesman Dawoud Shehab said.
Israel was examining Egypt's proposals, Foreign Minister Eli Cohen told public broadcaster Kan.
Prime Minister Benjamin Netanyahu said in broadcast remarks that Islamic Jihad had sustained a serious blow, but cautioned: "The campaign is not over yet."
The Israeli military said it hit more than 130 targets, including rocket-launching sites, as blasts sounded across the Palestinian enclave.
A late-night bombing of a building in the southern Gaza area of Khan Younis killed the head of Islamic Jihad's rocket launching force, identified as Ali Ghali, and two other militants, the Israeli military and Islamic Jihad said.
Minutes after Wednesday's air-strikes began, sirens sounded in Israel - mostly among border communities but soon also in and around the commercial capital Tel Aviv, 60 km (37 miles) north of Gaza.
More than 400 rockets were fired, Netanyahu said, a quarter of which fell short in Gaza.
The joint command of Gaza's militant groups, which includes Islamic Jihad and the enclave's Hamas rulers, claimed responsibility for the salvoes.
However Israeli military officials said they had seen no signs that Hamas, which is believed to have hundreds of rockets in its arsenal, had fired any missiles itself.
They said Israeli strikes were directed only at targets linked to the smaller Islamic Jihad group, an Iranian-backed militant organization based in Gaza which has been increasingly active in the occupied West Bank for the past year.
White House national security advisor Jake Sullivan emphasised the need for de-escalation during a call on Wednesday with the head of Israel's National Security Council, Tzachi Hanegbi, the White House said.
"Sullivan ... noted continued regional efforts to broker a ceasefire, and emphasized the need to deescalate tensions and prevent further loss of life," according to a White House readout.
CHILDREN AMONG FATALITIES
In total, 24 Palestinians, including at least five women and five children, as well as three senior Islamic Jihad commanders and four gunmen have been killed since fighting began, Palestinian health officials said.
Among the fatalities on Wednesday was a 10-year-old girl, although the circumstances of her death were unclear.
The militant groups said the rocket salvoes were a retaliation for the Israeli strikes, which it described as "a savage and treacherous bombardment of civilian houses that led to several innocent martyrs."
Multiple trails could be seen ascending over Gaza as rockets were launched. Mid-air explosions signalled interceptions by Israel's Iron Dome aerial defence system and there were no reports of casualties in Israel.
Last week, Islamic Jihad fired more than 100 rockets across the border and Israeli jets hit targets in Gaza in an hours-long exchange following the death of an Islamic Jihad hunger striker in Israeli custody.
Even before Wednesday's rocket barrage began, as many as 30% of residents of Israeli border communities had been evacuated as a precaution, municipal head Gadi Yarkoni told Kan radio.
In Gaza, businesses and schools remained closed, Israel kept its two commercial and people crossings with Gaza closed. The move would stop the entry of goods, fuel and humanitarian aid as well as patients who receive treatment in hospitals in the West Bank and Israel.
Earlier on Wednesday, Israeli forces killed two Palestinian gunmen who the military said had opened fire on them in the West Bank. Islamic Jihad claimed the men as members.