JERUSALEM  — Gaza militants fired dozens of rockets at southern Israel early on Tuesday, killing a man in a strike on a residential building, and warning they would escalate their attacks if Israel continues bombing targets in the Gaza Strip.

The cross-border attacks, which were triggered by a botched Israeli undercover raid into Hamas-ruled Gaza late Sunday, marked the most serious escalation since an Israel-Hamas war in 2014.

International mediators appealed for restraint, hoping to avert another war.

The Israeli military said some 400 rockets and mortars have been launched from Gaza since the current round began on Monday afternoon, with about 100 of them intercepted by Israel's Iron Dome defense system.

Israel has hit more than 100 targets it says are linked to militants in Gaza, including a strike that destroyed the TV station of Hamas, the Islamic militant group that rules Gaza.

On Tuesday, Gaza's health ministry said two Palestinians in their 20s were killed in separate airstrikes, raising the number killed since the Israeli offensive began Monday to six, including four militants. At least 25 people have been wounded.

Israeli medical officials said a 48-year-old man was found early Tuesday under the rubble of a building hit by a rocket in the southern city of Ashkelon. Relatives in the West Bank town of Halhoul identified the man as Mahmoud Abu Usbeh, a Palestinian laborer who had been working in Israel. He left a wife and six children behind.

"Everyone in town is sad. It's God's will and there nothing we can do about it," said his cousin, Jihad Abu Usbeh.

At least 20 people have also been wounded in Israel, three critically, according to medical officials.

The military said jets struck several "key strategic" Hamas targets, including military compounds, rocket launching posts and part of its vast underground tunnel network. Also targeted was a Gaza City building serving Hamas' military and intelligence forces that houses a munition warehouse.

The armed wing of Hamas threatened to step up its attacks and fire rockets further north toward the Israeli cities of Ashdod and Beersheba if Israel continued its airstrikes.

The spokesman for the Hamas military wing, identified only as Abu Obeida, said the deadly attack on the coastal city of Ashkelon showed the city "has entered the range of fire as a response to the bombing of buildings in Gaza." He said Ashdod and Beersheba "are the next targets if the enemy continues bombing civilian buildings."

School has been cancelled in large parts of southern Israel and a local election has been postponed because of the threat of further attacks.

Over the past few months, the sides have come close to a major escalation several times, only to step back in favor of giving a chance to a long-term Egyptian mediated truce.

However, the current level of escalation and angry rhetoric, including Hamas' warnings to strike deeper inside Israel, might make it more difficult to restore calm.

The Israeli security Cabinet began meeting to discuss the next steps, as the United Nations appealed for calm and said it was trying to broker a cease-fire.

The eruption of fighting cast doubt over recent understandings brokered by Egypt and U.N. officials to reduce tensions. Earlier this week, Israeli Prime Minister Benjamin Netanyahu had defended those understandings, saying he was doing everything possible to avoid another war. But he will now be under intense pressure to retaliate, given Hamas' unrelenting rocket barrages.

The rocket fire was triggered by a botched Israeli military raid in Gaza on Sunday. Undercover troops, apparently on a reconnaissance mission, were discovered inside Gaza, setting off a battle that left seven militants, including a Hamas commander, and a senior Israeli military officer dead. Hamas then fired a guided missile that struck a bus from which soldiers had just disembarked, an upgrade over its typical inaccurate projectiles.

The strike set the bus on fire, sending a large plume of black smoke over the area. A 19-year-old soldier was critically wounded and rocket attacks and Israeli retaliation fire quickly ensued.

The airstrikes and rocket barrages resumed at dawn Tuesday after nearly two hours of calm.

Lt. Col. Jonathan Conricus, a military spokesman, said Israeli warplanes, tanks and naval vessels were involved in strikes against military compounds, observation posts and weapons facilities belonging to the two main Gaza militant groups behind the attacks — Hamas and the Islamic Jihad.

He said the Israeli military has enhanced its deployment along the border but had yet to mobilize its reserves. He said Gaza militant groups were believed to have an arsenal in excess of 20,000 rockets and mortars of different caliber and range.

In Gaza, schools and public institutions were closed as people ventured outside to inspect the damage after a long night of aerial raids. Near the destroyed TV station, residents salvaged papers and belongings from their damaged houses. Debris was strewn across the streets and shattered window glass crunched under people's feet.

In Gaza City's Rimal neighborhood, a six-story residential building that also housed a kindergarten on its ground floor was destroyed.

"All the people here are civilians, children and families. We took our children and fled from here. When we returned, we found great destruction," said Mamdouh al-Shurafa, a resident of the building. "When we are bombed in the middle of the city, where we can go?"

Israel and Hamas have fought three wars since the Islamic militant group seized control of Gaza from the internationally-backed Palestinian Authority in 2007. In the most recent war, over 2,200 Palestinians were killed, more than half of them civilians, and tens of thousands were left homeless. Seventy-three people, most of them soldiers, were killed on the Israeli side.

Israel and Egypt have maintained a blockade on Gaza since the Hamas takeover, a blockade that has devastated Gaza's economy.

In recent weeks, Egyptian and U.N. 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 has lowered the intensity of its border protests in recent weeks.

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