The fighting - which has killed six Palestinians, five of them militants, and a civilian in Israel since Monday - threatened to derail efforts by the United Nations, Egypt and Qatar to broker a long-term truce and head off another major conflict.
One person was killed and at least 20 others were wounded in a massive Palestinian rocket barrage targeting southern Israel on Monday.
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. One Palestinian witness said Gaza was slammed with as many as40 airstrikesin less than an hour as the Israeli team fled the besieged Gaza Strip, which is in the midst of a severe humanitarian crisis due to decades of brutal Israeli occupation. It maintains a blockade on Gaza's coastline and has destroyed its airport, preventing any air transport in and out of the territory.
The salvoes were the fiercest since the seven-week Gaza war in 2014 between Israel and Gaza militants.
Israel said the outlet "contributes to Hamas's military actions". Near the destroyed TV station, residents salvaged papers and belongings from their damaged houses.
Egypt, which borders Gaza to the south, urged Israel to back down. Another rocket landed near a factory, and several homes were hit in southern towns.
The David Magen Adom emergency service said a 19-year-old young man was "in a serious condition with multi-system injuries".
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A spokesman for Hamas's military wing, Abu Obeida, warned on Twitter of harsher strikes to come if the Israeli attacks continue, and Palestinian President Mahmoud Abbas cut short a trip to Kuwait and his office said he held "intensive regional and worldwide contacts" to try to stop Israel's assaults. After the strike on the television station, Palestinian factions said they would extend the range of their rockets.
Since March, more than 200 Palestinians have been martyred and thousands more injured by Israeli army fire during protests demanding the right of Palestinian refugees to return to their ancestral home in what is now Israel.
A Hamas spokesman said: "In response to yesterday's crime, the joint command of Palestinian factions announce the beginning of bombardment of the enemy's settlements with scores of rockets". It said militants discovered the vehicle and chased it down, prompting Israeli airstrikes that killed "a number of people".
The Israeli military remained tight-lipped about the incident but said a covert operation had been underway at least 2 miles inside the Gaza Strip when the unit's presence was somehow blown.
Last week, Israel allowed Qatar to deliver $15 million in aid to Gaza's cash-strapped Hamas rulers.
Israeli military chief, Lt. Gen. Gadi Eisenkot said a "special force" carried out "a very meaningful operation to Israel's security", but did not provide further details. At the same time, Hamas has lowered the intensity of the 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.
In a tweet after his arrival, Netanyahu praised the slain officer, whose funeral was held Monday, and said "our forces acted courageously".