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.
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.
Sirens wailed across Jerusalem just after the 3 p.m. GMT deadline set by Hamas as people in the city, including lawmakers in the Knesset legislature, fled to bunkers for the first time since the 2014 Gaza conflict.
Prime Minister Benjamin Netanyahu said Hamas had "crossed a red line" by targeting Jerusalem and vowed that the Jewish state would "respond with force."
Hamas' Qassam Brigades said, "this is a message that the enemy must understand well: if you respond we will respond, and if you escalate we will escalate."
Several properties in Israel have been damaged by rockets, including an apartment in the southern city of Ashkelon, and a house in Beit Nekofa, west of central Jerusalem.
An Israeli Arab died from gunshot wounds in clashes with Israeli Jews in the central city of Lod, police said Monday, without providing details.