In the past, cross-border fighting between Israel and Hamas, the group that rules Gaza, would typically end after a few days, often helped by behind-the-scenes mediation by Qatar, Egypt and others. It was not clear if such a resolution would come this time.
Israeli prime minister Benjamin Netanyahu has warned that fighting could "continue for some time".
Lt Col Jonathan Conricus, an Israeli military spokesman, told reporters on Tuesday that the military was in "the early stages" of strikes against Gaza targets that it had planned well in advance.
The overnight rockets and strikes were preceded by hours of clashes between Palestinians and Israeli security forces, including dramatic confrontations at Jerusalem's al-Aqsa Mosque compound, a sacred site to both Jews and Muslims.
In fighting in the contested city and across the West Bank, more than 700 Palestinians were hurt, including nearly 500 who were treated at hospitals.
In a sign of widening unrest, hundreds of residents of Arab communities across Israel staged overnight demonstrations - denouncing the recent actions of Israeli security forces against Palestinians - in one of the largest protests by Palestinian citizens in Israel in recent years.
The escalation comes at a time of political limbo in Israel.
Mr Netanyahu has been acting as a caretaker prime minister since an inconclusive parliamentary election in March. He tried and failed to form a coalition government with his hard-line and ultra-Orthodox allies, and the task was handed to his political rivals last week.
One of those rivals is Israel's defense minister who is overseeing the Gaza campaign.
It is not clear if and to what extent the toxic political atmosphere is spilling over into military decision-making, though the rival camps have unanimously expressed support for striking Hamas hard.
Israeli media have reported that the new round of violence is slowing efforts by Netanyahu's rivals to form a ruling coalition among parties with a broad range of ideologies, but a shared goal of toppling Mr Netanyahu.
The support of an Arab-backed party with Islamist roots is key for the anti-Netanyahu bloc's efforts.
The party's leader, Mansour Abbas, has essentially said he'll work with whatever political camp offers the most improvements in Arab communities, but the current tensions might deter him from joining a coalition, at least for now.
The current round of violence in Jerusalem coincided with the start of the Muslim fasting month of Ramadan in mid-April.
Critics say heavy-handed police measures helped stoke nightly unrest, including a decision to temporarily seal off a popular gathering spot where Palestinian residents would meet after evening prayers.
Another flashpoint was the Jerusalem neighborhood of Sheikh Jarrah, where dozens of Palestinians are under threat of eviction by Jewish settlers.
Over the weekend, confrontations erupted at the Al-Aqsa Mosque compound, which is the third holiest site of Islam and the holiest site in Judaism.
For four successive days, Israel police fired tear gas, stun grenades and rubber bullets at Palestinians, who hurled stones and chairs.
Hundreds of Palestinians were hurt, requiring treatment at hospitals. Two dozen officers were also injured. At times, police fired stun grenades into the carpeted mosque.
On Monday evening, Hamas began firing rockets from Gaza, setting off air raid sirens as far as Jerusalem, after giving Israel a deadline to withdraw Israeli security forces from the compound. From there on, the escalation was rapid.
Mr Conricus, the army spokesman, said Gaza militants fired more than 250 rockets at Israel, with about one-third falling short and landing in Gaza.
The army said that a rocket landed a direct hit on a seven-storey apartment block in the coastal Israeli city of Ashkelon. Photos and videos from the scene showed a large hole in the side of the building. Israeli paramedic service Magen David Adom said it treated six people injured in the rocket strike. Two were hospitalized in moderate condition.
Mr Conricus said the military hit 130 targets in Gaza, including the high-rise home of a Hamas field commander and two tunnels militants were digging under the border with Israel.
In all, Israel killed 15 militants, Mr Conricus said. He said Israel's new system of concrete barriers and electronic sensors, intended to thwart tunnel digging, has proven effective.
He did not address Gaza health ministry reports that nine children were among 24 Palestinians killed overnight.
In Gaza, most of the deaths were attributed to Israeli airstrikes.
However, seven of the deaths were members of a single family, including three children, who died in an explosion in the northern Gaza town of Beit Hanoun and it was not clear if the blast was caused by an Israeli airstrike or an errant rocket.
More than 100 Gazans were wounded in the airstrikes, the health ministry said.
In one, an Israeli missile hit the upper floors of an apartment building in the Shati refugee camp on the edge of Gaza City early on Tuesday, killing two men and a woman inside, according to health officials.
Israel had struck scores of Gaza homes in its 2014 war with Hamas, arguing it was aiming at militants, but also killing many civilians. The practice drew broad international condemnation at the time.
Israel's tactics in Jerusalem have drawn angry reactions from the Muslim world.
Regional power house Saudi Arabia said in a statement that it condemns in the strongest terms what it said were attacks by Israeli forces against the sanctity of Al-Aqsa and the safety of its worshippers.
The Saudi foreign ministry called on the international community to hold Israeli forces responsible for any escalation.
Separately, the 57-nation Organization of Islamic Cooperation is holding an emergency meeting of its permanent representatives in Jeddah to discuss the tensions.
Rockets fired from Gaza killed two women in the southern Israeli city of Asheklon on Tuesday, as Prime Minister Benjamin Netanyahu vowed to increase the intensity and frequency of its attacks on the territory.
A Magen David Adom emergency service spokesman told AFP that one of the dead women was in her 40s and the other in her mid-60s, adding that they were killed in separate incidents after a barrage of rockets from Gaza.
The news came as Israel unleashed fresh airstrikes on Gaza on Tuesday morning, killing at least 26 Palestinians and hitting the high-rise home of a Hamas field commander and two border tunnels dug by militants.
In a further sign of rising tensions, Israel signaled it was widening its military campaign. The military said it is sending troop reinforcements to the Gaza border and the defense minister ordered the mobilization of 5,000 reserve soldiers.
Mr Netanyahu said after meeting with senior defense officials that Israel would "increase even more the strength of the strikes and also the rate of the strikes" against Hamas and Islamic Jihad militants in the Gaza Strip.
"Hamas will receive blows now that it didn't expect," he said in a statement.
The escalation in the conflict was sparked by weeks of tensions in contested Jerusalem.
Since sundown Monday when the cross-border attacks began, at least 26 Palestinians - including nine children - have been killed in Gaza, most by airstrikes, Gaza health officials said. The Israeli military said 15 of the dead were militants.
During the same period, Gaza militants fired more than 250 rockets toward Israel, injuring six Israeli civilians in a direct hit on an apartment building.
The UN High Commissioner for Human Rights said Tuesday it was "deeply concerned" over the escalation of violence and called for any use of force to comply fully with international human rights standards.
"Things need to calm down," spokesman Rupert Colville told reporters in Geneva.