Israeli Prime Minister Benjamin Netanyahu said late Tuesday that they "will continue the attack on Gaza with full force" while Defense Minister Benny Gantz vowed to intensify air campaign, saying "this is just the beginning."
The Premier also added that the Israeli military operation "has dealt a tough blow" to Palestinian resistance group Hamas, which runs the Gaza Strip, underlining that the fighting will continue for some time.
In a nationally televised speech late on Tuesday, he claimed that Hamas and Islamic Jihad "have paid, and will pay a heavy price."
He said Israel will press ahead with an intensified operation, but said "it will take time" to complete the mission.
Israel's Iron Dome air defense system struggled as most of the rockets fell unintercepted amid increasing number of clashing missiles, local media said late Tuesday.
Meanwhile, the number of Israelis wounded by rockets rose to 26.
Earlier on the same day, the death toll of Palestinian civilians killed in Israeli airstrikes on blockaded Gaza Strip rose to at least 28, including children amid an escalation sparked by violent unrest at Jerusalem's flashpoint Al-Aqsa Mosque compound.
10 children and one woman were among those killed in the blockaded Gaza that is controlled by Hamas and 152 people there were wounded, Palestinian Health Ministry said.
Two Israeli women were also killed by rockets fired from Gaza in response to recent Israeli aggression in the heavily-targeted coastal city of Ashkelon, just north of Gaza, said the emergency service Magen David Adom. The local Barzilai medical center said it was treating 70 injured.
Hamas' Qassem Brigades had vowed to turn the town "to hell" and rained down an intense volley, claiming to have fired 137 rockets towards Ashkelon and nearby Ashdod within just five minutes. Loud booms again rocked the town on Tuesday, where a rocket had ripped a gaping hole into the side of an apartment block, an Agence France-Presse (AFP) reporter said.
Over 90% of recent rockets from Gaza were reported intercepted by the Iron Dome missile defense system, Israeli army spokesperson Jonathan Conricus said earlier.
Israel fighter jets and attack helicopters have carried out more than 130 strikes on military targets in the enclave, said Conricus. Israeli officials said they have killed 15 Hamas commanders, while the group Palestinian group Islamic Jihad confirmed two of its senior figures were also killed.
Later on Wednesday, Gantz vowed more attacks on Gaza to bring "total, long-term quiet" before considering a ceasefire.
"The army will continue to attack to bring a total, long-term quiet. Only when we reach that goal will we be able to speak about a truce," Gantz said in Ashkelon.
"We don't need moral lessons from other countries. All military options are on the table to deal with the problem in Gaza."
Tensions in Jerusalem have flared into the city's worst disturbances since 2017 in the days since Israeli riot police clashed with large crowds of Palestinians on the last Friday of the Muslim holy fasting month of Ramadan.
Nightly unrest since then at the Al-Aqsa compound in occupied East Jerusalem has left more than 700 Palestinians wounded, drawing international calls for de-escalation and sharp rebukes from across the Muslim world.
Hamas had Monday warned Israel to withdraw all its forces from the mosque compound and the East Jerusalem district of Sheikh Jarrah, where the looming forced expulsion of Palestinian families has fuelled angry protests.