The hostilities amount to the heaviest fighting between the two sides in months.
Gaza’s health ministry said seven people were killed on Wednesday, a day after Israeli strikes on the Palestinian territory left 15 dead.
Four of those killed on Wednesday were fighters with the Popular Front for the Liberation of Palestine, the group said.
Three more deaths were reported following an air attack in the early hours of Thursday morning in Khan Younis in the southern part of Gaza.
A 10-year-old Palestinian girl named Layan Madoukh was also killed in a blast at her home in Gaza City in unclear circumstances.
“There is a very high sense of worrying,” Al Jazeera’s Youmna El Sayed, reporting from Gaza City, said.
“Everything is closed; schools, private and public facilities have shut down, and people have limited going out of their homes.”
Rana Shubair, a Gaza-based writer, said that the Israeli attacks took them “by surprise completely”.
“Everybody was asleep; we suddenly work up to huge explosions,” she told Al Jazeera.
“Barrages of rockets are being launched from the Gaza Strip towards southern Israeli towns,” Sayed added. “We also saw the Iron Dome trying to intercept these rockets.”
The hostilities amount to the heaviest fighting between the sides in months.
Israeli officials said more than 400 rockets had been fired as of Wednesday evening. Most, they said, were intercepted or fell in open areas, but Defence Minister Yoav Gallant said about one-quarter had misfired and fallen inside Gaza.
Journalist Issam Adwan, reporting for Al Jazeera from Gaza City, said that after a “cautious silence” that had lasted around two hours late on Wednesday and into the early hours of Thursday morning, Israel renewed its air attacks with two strikes on Gaza’s Khan Younis, one of which hit a residential apartment building.
The Ministry of Health confirmed three deaths and dozens of people injured, Adwan said.
“So after this cautious silence, now it’s broken with another round of violence from the Israeli air strikes,” he said.
“It is very difficult to cope in these circumstances for [Palestinians in Gaza],” he added.
“The city is basically crippled and citizens are expecting the worst.”
The Israeli military said later that it had hit members of the Palestinian Islamic Jihad movements, killing the commander of the group’s ‘rocket launching unit’.
United Nations Secretary-General Antonio Guterres condemned civilian deaths in Gaza as “unacceptable” and appealed for them to “stop immediately” and for all parties to exercise maximum restraint, deputy UN spokesperson Farhan Haq said on Wednesday.
“Israel must abide by its obligations under international humanitarian law, including the proportional use of force and taking all feasible precautions to spare civilians and civilian objects in the conduct of military operations,” Haq said.