Rocket alarms rang out across southern Israel as dawn broke Tuesday and into the morning, ending a brief overnight lull, as intense fighting between Gaza terrorist groups and Israel entered its second day.

Rocket were launched from Gaza at Ashkelon and towns closer to the Gaza border, including Sderot. Two houses in the Eshkol region were hit by rockets. There were no immediate reports of injuries.

The fresh barrage came after several hours of relative quiet in Israel following an unprecedented and deadly bombardment from Hamas-run Gaza on Israeli towns near the border that forced most Israelis in the area to spend the night in bomb shelters and brought the sides back to the brink of war.

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The Israel Defense Forces said before the fresh barrage Tuesday that about 370 rockets and mortar rounds had been shot at Israel since Monday, including 70 rockets fired at Israeli towns since midnight, in what was being called the largest-ever barrage on southern Israel. The rockets fired Tuesday morning pushed that figure beyond 400.

The IDF said dozens of rockets had been knocked down by the Iron Dome anti-missile system overnight, and “about 100” had been intercepted since the rocket volleys began Monday afternoon.

While most of the rockets shot at Israel that were not intercepted by Iron Dome landed in open areas, several scored hits on homes and other buildings.

The rocket fire had tapered off at around 1:30 a.m. Several rocket alert sirens sounded in communities near the Gaza border just after 4 a.m., but there were no reports of impacts.

In Gaza, there were reports of continuing Israeli airstrikes overnight, after a day that saw dozens of Israeli reprisal attacks across the Strip, including in populated areas. The IDF said Tuesday that it had hit 150 targets across Gaza since the day before, including sites belonging to Hamas, which rules Gaza, and Islamic Jihad, a smaller terror group.

The military said it struck weapons warehouses, a naval vessel used by Hamas and a building used as the administration of Hamas’s internal security service overnight.

In a statement, the army said the security service “leads continuous attempts to carry out terror attacks in Israel.”

The Hamas-run health ministry said four people were killed, three of whom were identified as members of terror groups.

In the coastal city of Ashkelon, which took on several barrages late Monday and early Tuesday, one person was killed when an apartment building was hit around midnight. Eight others were wounded in the strike, including two women with life-threatening injuries, according to emergency services.

Unconfirmed reports in Hebrew media identified the sole fatality in Israel as a West Bank Palestinian living in Israel without documentation.

In all, more than 50 Israelis were treated for injuries since Monday, most of them light wounds or stress-related trauma, authorities said.

Spokespeople for the armed wing of Hamas, the terror group that runs the Strip, threatened to start shooting rockets deeper into Israeli territory if fighting continued, calling the barrages on Ashkelon a “warning.”

“Approximately one million Zionists will be within the range of our missiles if the Zionist enemy’s decision is to continue its aggression,” a spokesman said.

Another spokesman said Tuesday morning that if Israel will continue its bombardments of Gaza, “Ashdod and Beersheba are next in line.”

Israel issued warnings of its own and indicated it would not back down.

Lt. Col. Jonathan Conricus, a military spokesman, said the army had sent additional infantry troops, rocket defense systems and intelligence units to the Gaza frontier.

“We continue to strike and retaliate against the military targets belonging to terrorist organizations in Gaza, and as for our intentions we will enhance these efforts as needed,” he told reporters.

IDF Spokesman Brig. Gen. Ronen Manelis tweeted that “Hamas knows well what our targets are and what the price of conflict with the IDF is.”

The fighting cast doubt over recent understandings brokered by Egypt and UN officials to reduce tensions. Just a day earlier, Prime Minister Benjamin Netanyahu had defended those understandings, saying he was doing everything possible to avoid another war.

The United Nations said it was working with Egypt to broker a halt in the violence. “Rockets must STOP, restraint must be shown by all!” the UN Mideast envoy’s office tweeted.

UN Secretary-General Antonio Guterres, meanwhile, urged Israel and the Palestinians “to exercise maximum restraint,” according to a statement.

The rocket attacks began shortly after 4:30 p.m. Monday, when terrorists fired a Kornet anti-tank guided missile at an Israeli bus near the border, seriously injuring an IDF soldier who standing near it at the time. Dozens of other soldiers had previously been on the bus, parked near the Black Arrow memorial near Kibbutz Kfar Azza, and exited moments before the missile struck.

In response to the attacks, the Israeli military launched a series of strikes against dozens of targets inside the Gaza Strip, including multi-story buildings housing a Hamas military intelligence center and the headquarters of al-Aqsa TV.

The army also said it targeted three attack tunnels operated by Hamas and the Palestinian Islamic Jihad, the two largest terror groups in the Strip.

On Monday evening, large numbers of tanks and other military vehicles were seen being moved down to the Gaza border on the backs of large trucks. Earlier in the day, before the barrages began, the army also ordered extra infantry battalions to the region.

Additional Iron Dome air defense batteries were also deployed in southern Israel on Monday morning.

The barrages from Gaza came less than a day after an IDF special forces officer was killed in an operation gone awry that also killed seven Palestinian gunmen in the Strip. Following Sunday night’s incident, Hamas said “the blood of our righteous martyrs will not be wasted.”

In light of the barrage from the Gaza Strip, the Israeli military ordered residents of communities near the Gaza Strip to remain inside bomb shelters until further notice. That included residents of the towns of Netivot and Ofakim, which are not typically as affected by Gaza rockets as communities closer to the border.

Residents of the cities of Beersheba, Ashkelon and Ashdod were told to stay within close proximity of bomb shelters and protected spaces.

A run-off election scheduled for Tuesday in the Hof Ashkelon region was postponed.

The military also preemptively canceled school for Tuesday in the Gaza border region and in the central Negev and Lachish regions, including in Israel’s fourth largest city Beersheba.

In addition, businesses were ordered closed in the Gaza region, along with government offices, unless they are considered essential, the army said. No large gatherings were allowed in southern Israel on Monday night and Tuesday, it said.

In the central Negev and Lachish regions, which are farther from the Strip, businesses are only ordered shut if they do not have a bomb shelter nearby. Government services there were also scaled back.

In those regions, located dozens of kilometers from Gaza, only groups smaller than 300 would be allowed to gather on Tuesday, the army said.

In Gaza, Hamas set up multiple checkpoints in a show of force. It also restricted movement through crossings with Israel, preventing foreign journalists, local businessmen and some aid workers from leaving the territory.

Hamas also canceled a weekly beach protest in northwestern Gaza along the border with Israel. The organizers cited “the ongoing security situation.”

In recent weeks, Egyptian and UN mediators had appeared to make progress in brokering informal understandings aimed at quieting the situation.

Last week, Israel allowed Qatar to deliver $15 million to Gaza to allow cash-strapped Hamas to pay the salaries of thousands of government workers. At the same time, Hamas, which seized control of Gaza in 2007 and seeks to destroy Israel, has lowered the intensity of the border protests in recent weeks.

Netanyahu cut short a visit to Paris because of the flareup and returned to Israel on Monday for consultations with top security officials.

A meeting of top ministers in the security cabinet was scheduled for Tuesday morning.

On Sunday, Netanyahu defended his decision to allow through the Qatari cash to Gaza as a way to avert an “unnecessary war,” maintain quiet for residents of southern Israel and prevent a humanitarian catastrophe in the impoverished Gaza Strip.