Palestinian President Mahmoud Abbas condemned the violence in the Gaza Strip, charging Israel with escalating tension in the region, in remarks reported by Palestinian media on Sunday.
Abbas spoke by phone to Hamas and Islamic Jihad leaders, as well as with Arab and international mediators, in a bid to end the worst violence since October, DPa reported.
Ismail Haniya, Gaza's de-facto Hamas prime minister, said in a statement that Hamas was also holding intensive contacts with various parties to stop the violence.
Local observers said Hamas security forces were seeking to regain control of the situation after initially allowing Palestinian militants to avenge the targeted killing of a leading militant by Israeli forces on Friday.
Earlier Sunday, Israel launched airstrikes on the Gaza Strip in response to continuing rocket fire from across the border. Three Palestinians, including a 12-year-old boy on his way to school, were killed, Gaza emergency services chief Adham Abu Salmiyeh said.
The cross-border tit-for-tat followed the killing of Palestinian militant Zohair al-Qaisi, the secretary-general of the radical Popular Resistance Committees (PRC).
"On Friday an arch-terrorist was killed who had organized many attacks against Israel and was in the midst of another action, a terrorist action directed at our southern, joint border with Egypt," Israeli Prime Minister Benjamin Netanyahu told the cabinet on Sunday.
"There is no doubt that the action by the Israel Defence Forces thwarted this plot," Netanyahu said, according to a statement from his office.
He added the killing had sparked an expected round of violence by the PRC, Islamic Jihad and other militants, but that Israel was making them pay a "heavy price."
The Israel Air Force fired at two groups of militants in northern Gaza that were about to launch rockets into southern Israel during the early hours of Sunday, a military spokeswoman in Tel Aviv said.
A militant was killed south-east of Gaza City, near the border with Israel, while a 52-year-old died in a strike north-east of the city. Local residents said he was a civilian minding a citrus orchard.
The 12-year-old boy died when a group of children on their way to school east of the Jabalya refugee camp were hit by shrapnel. A 7-year-old was also injured in the incident.
Palestinians have fired at least 127 rockets and mortar shells at southern Israel since Friday, resulting in at least five people being hospitalized - including a Thai worker who was in a serious condition.
Israel responded by launching 21 airstrikes at militants firing the rockets, as well as at weapons caches and workshops, killing 18 Palestinians - 16 militants and two civilians - since Friday, Gaza officials said. At least 30 Palestinians have been wounded.
The Israeli Iron Dome missile defence system shot down 37 of 43 Russian-type Grad missiles fired toward the southern Israeli cities of Ashdod, Ashkelon and Beersheba, the army said. One missile nevertheless landed in a street in Beersheba Sunday afternoon.
The violence erupted Friday afternoon when the Israel Air Force hit a vehicle in Gaza City that was carrying al-Qaisi. A second militant also died in the attack.
The military accused al-Qaisi of planning a major attack on Israel from the Sinai. He also allegedly ordered the attack on an Israeli road near Egypt in August, not far from the Red Sea resort of Eilat. Eight Israelis died in that attack.
Egypt is trying to broker a new truce between Israel and the Gaza Strip, which is ruled by Hamas.