Israel and militants in the Gaza Strip have stepped up their attacks on each other, in some of the most intense exchanges of recent years.
The army says Palestinian militants have fired 600 rockets into Israeli territory over the weekend. Many were intercepted but three Israelis died.
Israel says it has hit 260 targets in the Gaza Strip and threatened further "massive" strikes.
At least 15 people have died so far in Gaza, the Health Ministry there says.
On Sunday, Israeli Prime Minister Benjamin Netanyahu said he had ordered the military to "continue its massive strikes on terror elements in the Gaza Strip".
Israeli forces around Gaza would be "stepped up with tank, artillery and infantry forces", he added.
The flare-up comes despite a truce agreed last month. Egypt and the United Nations have recently been trying to broker a longer-term ceasefire.
The violence began on Friday, during protests in Gaza against the blockade of the area - which Israel says is needed to stop weapons reaching militants.
A Palestinian gunman shot and wounded two Israeli soldiers at the boundary fence. Israel retaliated with an air strike that killed two militants.
The rocket barrage from Gaza began on Saturday morning. Israel's Iron Dome missile defence system shot down dozens of the rockets, but a number of homes in Israeli towns and villages were hit.
Barzilai Hospital in Ashkelon, 10km north of Gaza, has said it has treated more than 100 civilians in the past 24 hours.
Out of those, three people died and three more were seriously wounded - including an elderly Israeli woman.
Those killed included a 58-year-old man struck in a garden, Israeli media say.
Israel air strikes targeted sites belonging to the militant groups Hamas and Islamic Jihad on Saturday and Sunday.
On Sunday, the Israeli military said they had killed a Hamas commander named Hamed Hamdan al-Khodari in one of their strikes.
Gaza's Health Ministry say the 15 killed there include two pregnant women and an infant.
Israel has contested the account of the death of one woman and her 14-month-old niece killed on Saturday. They blamed their deaths on a Palestinian rocket that fell short of its target.
The sites destroyed include a multi-storey building in Gaza City, which Israel said included Hamas intelligence offices.
Hamas paying 'heavy price' for rocket attacks - Netanyahu
Israeli Prime Minister Benjamin Netanyahu said Hamas was paying a "heavy price" for its rocket attacks against Israel and that it would be held accountable not only for its own militant actions but also for that of the Islamic Jihad, which operates under its jurisdiction in Gaza.
Sirens wailed along the border region overnight warning of incoming attacks. School was cancelled in southern Israel and emergency protocol enacted.
In Gaza, large explosions thundered across the blockaded enclave during the night as plumes of smoke rose into the air. One of the airstrikes hit a six-story commercial and residential building that housed the office of Turkey's official Anadolu news agency. Foreign Minister Mevlut Cavusoglu called it a "new example of Israel's unrestrained aggression."
The Israeli military says its Iron Dome defense system intercepted more than 150 of the projectiles from Gaza, but several still managed to slip through. A rocket scored a direct hit on a residential home in the border town of Sderot.
Jonathan Rieck, director of the emergency room at Barzilai Medical Center in Ashkelon, said they had treated some 80 people, most from shock symptoms, but several with body wounds, including an elderly man who was in critical condition from head injuries.
Israel has vowed to hit back hard against both Hamas and Islamic Jihad, whom it suspects of triggering the current conflagration. But, as in similar previous rounds where it stopped short of a full-fledged war, the timing for a prolonged round of fighting is tricky for Israel.
The country marks Memorial Day and Independence Day this week, when masses head out to ceremonies at military cemeteries and then street parties across the country. The following week it is set to host the Eurovision song contest in which large groups of tourists are expected to arrive for the campy spectacle.
For Gazans, the violence comes ahead of the Muslim holy fasting month of Ramadan that begins on Monday.
Hamas, an Islamic group vowed to Israel's destruction, forcefully seized control of Gaza in 2007. It most recently engaged in several days of heavy fighting with Israel in March before Egypt brokered a truce, in which Israel agreed to ease a crippling blockade on Gaza in exchange for a halt in rocket fire.
Israel and Hamas trade accusations
In recent days, Hamas accused Israel of reneging on its pledges as militants began to fire rockets into Israel. Israel in turn accuses Islamic Jihad of instigating the latest round of violence by shooting and wounding two Israeli soldiers on Friday.
Though it says the shooting was not coordinated with Hamas, and that Islamic Jihad has been undermining Hamas of late, Israel still holds Hamas responsible for all the fire as the territory's ruling power.
Yaakov Amidror, a former Israeli national security adviser, said the source of the eruption of violence was Islamic Jihad militants in Gaza being pushed by their patrons in Tehran.
"This is the interest of the Iranians, that there will be another operation in Gaza that they will be free to continue what they are doing in Syria and Israel will be busy with and focusing on Gaza," explained Mr Amidror, currently a senior fellow at the Jerusalem Institute for Strategy and Security.
Islamic Jihad has threatened to fire longer range rockets toward Israel's heartland, and in a video that also was seen as an implicit claim of responsibility, it showed archived footage of militants attaching warheads to rockets.
It threatened to shatter the shaky understandings recently reached though Egyptian mediators. Israel had agreed to expand a fishing zone off Gaza's coast, increased imports into Gaza and allow the Gulf state of Qatar to deliver aid to cash-strapped Gaza. Militant leaders were in Cairo trying to reach a new cease-fire.
On Friday, two Palestinians were fatally shot by Israeli forces during the weekly protests along Israel-Gaza perimeter fence. Palestinian militants also shot and wounded two Israeli soldiers along the border fence. No group claimed responsibility for the shooting. In response, Israeli aircraft carried out retaliatory strikes, killing two Hamas militants.
Hamas has hoped that Egyptian mediators could further ease the blockade, which has ravaged Gaza's economy. For over a year, the Islamic group has orchestrated mass demonstrations each week along the Israeli frontier to draw attention to Gaza's plight. More than 200 Palestinians and an Israeli soldier have been killed in the border protests.
- AP/ BBC