The offices of the Hamas-operated Al-Aqsa television channel were also hit by the IDF following warnings.
On Monday, more than 300 rockets from Gaza were launched into southern Israel, the country's military said.
UN Secretary-General Antonio Guterres on Monday urged all sides to exercise maximum restraint.
There was no word from the security cabinet session whether Israel would agree, and rocket attacks continued amid Israeli air strikes as the forum met.
Israel and Hamas have traded tit-for-tat attacks regularly during the past few months, often when Hamas launches rockets in response to lethal Israeli army fire on weekly protests at the frontier - where Palestinians have been calling for an end to the blockade - or on Hamas positions after.
However, the recent tension since Sunday appears to be escalade since Israeli forces continue to deploy more forces to the border with Gaza.
Israel and militants in Gaza traded rocket and mortar fire Monday, a flare-up of violence prompted by an Israeli military operation over the weekend that resulted in the deaths of seven Palestinians and one Israeli.
Netanyahu has come under criticism from members of his right-wing government for his decision to allowQatar to provide money to the Hamas-run Gaza Strip to pay for salaries and provide other support to ease a humanitarian crisis in the coastal enclave.
The heavy exchange of fire, which was 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.
The escalation came hours after Palestinians and Israelis buried combatants who were killed on Sunday night, after what Israeli news media described as an Israeli intelligence mission inside the Gaza Strip that went awry.
CNN To Sue Trump Over Banned Journalist Acosta
Earlier this year, Acosta complained that Sanders didn't give him enough opportunities to ask questions. It would be a " really strong lawsuit ", the attorney told Brian Stelter on CNN's "Reliable Sources ".
Islamic Jihad spokesman Daoud Shehab said the groups chose to retaliate for the deadly Israeli incursion "so the occupation and its supporters know that the lives of our sons come with a price". Israeli warplanes struck the Khan Younis area so the soldiers could retreat.
The raid and subsequent rockets follow several months of saber-rattling but relative calm between the two parties.
But by Monday, thick plumes of smoke were rising above Gaza and southern Israel.
One senior Israeli officer also was killed. It maintains a blockade on Gaza's coastline and has destroyed its airport, preventing any air transport in and out of the territory.
More than 170 demonstrators, most unarmed, have been killed by Israeli army fire in the confrontations in which some of the participants threw stones, burned tires or threw grenades toward Israeli forces.
Undercover Israeli special forces entered around two kilometres into the territory in a civilian auto near the southern Gazan city of Khan Younis, opening fire when they were discovered, the Al Qassam Brigades, Hamas's armed wing, said in a statement. Hamas responded by lowering the intensity of the border protest last Friday.
Prime Minister Benjamin Netanyahu raced back from First World War commemorations in France after Hamas hit back hard following a daring Israeli raid into Gaza that backfired.
Hamas is not only striking a new aggressive pose against Israel, it is also banking on a boost to its credibility in the Palestinian arena, through its willingness to clash head on with Israel, while it accuses the Palestinian Authority (PA), its hated domestic foe, of collaborating with Israel.
In a tweet after his arrival back home, Netanyahu praised the slain officer, whose identity was being kept confidential for security reasons, and said "our forces acted courageously".
Ismail Radwan, a Hamas official in the Gaza Strip, said that the Palestinian "resistance groups will halt all their activities once Israel stops its aggression".
White House officials said the decision was taken due to the weather and cited security concerns in hastily arranging a motorcade. Ben Rhodes, a top staffer for President Barack Obama , said there was "always" a backup bad-weather plan on presidential trips.
In the trailer, we get a look at Ryan Reynolds voicing Detective Pikachu (as well as the all too familiar Pika Pika voice). As the name of the move suggests, the movie is based around Pokemon's most recognisable figure, Pikachu .
Suheil al-Mazrouei, energy minister of the host country UAE, hinted that producers are preparing to cut output. "We need a consensus", he said , indicating that non-OPEC Russia would need to approve any decision.
A home left in ruins is shown through an iron gate in the aftermath of wildfires which devastated the area in Paradise . At least 31 people have died in the fires: 29 in the Camp fire and two in the Woolsey fire .
Oil prices rose by about one per cent on Monday after top exporter, Saudi Arabia, announced a cut in supply for December. Commerzbank, Germany's second-largest lender, said Friday oil producers must act to prevent a free fall of prices.
Stan Lee the creator of "Spider-Man", " Iron Man ", "X-Men" and numerous other superheroes passed away aged 95. Lee had graced many movies, comic books, video-games and sit-coms with his cameos, which were quite legendary.
More than 2,000 U.S. troops are buried at Aisne-Marne American Cemetery, where Trump was meant to visit on Saturday. Chief of Staff John Kelly , a retired Marine general, and Chairman of the Joint Chiefs of Staff Gen.
Stan Lee has been hailed a "creative genius" as a host of Hollywood stars paid tribute to the Marvel Comics co-creator. Chris Evans , a.k.a. " Captain America ", then kicked off a stream of effusive tweets from MCU actors and directors.
Stan Lee's creations are still the crown jewel of everything Marvel is known for in 2018, and certainly the foreseeable future. What a life and what a thing to have achieved. " Black Panther " star Letitia Wright simply said, "Rest in Peace Stan Lee ".
West Ham United unlikely to sign Samir Nasri?
But the former France worldwide has encountered a troubled career since, having been banned for 18 months by UEFA for doping . The ban concluded at the end of December, although Nasri has been free to train at a club from the beginning of November.
Strycova gives Czechs early lead in Fed Cup final
It was the ideal start for the Czechs, winners of five of the last seven Fed Cup titles, who are without two of their top players. In the second match, Siniakova cruised in the first set but fell behind in the second before pulling level at 3-3.
Israel hits Hamas TV station after shootout in Gaza
The group said that "the blood of the martyrs will not be without price" and "the battle between us and the enemy is continuing". These strikes represent an escalation in the IDF's response, as it has resorted to softer targets over the past few months.
Wildfires deadliest on record in California with 31 killed
At this desperate time, we would encourage the president to offer support in word and deed, instead of recrimination and blame". Residents who lost their Paradise homes to the Camp Fire came to Cherokee seeking refuge, only to face the same struggles.
Dozens of cat mummies found in 6,000-year-old tombs in Egypt
The Ministry of Antiquities verified with several museums around the world that no mummified scarabs have ever been discovered. Tourism in Egypt suffered in the aftermath of the mass protests that toppled former president Hosni Mubarak in 2011.