The armed wing of Hamas said the cities of Ashdod and Beersheba will be targeted next if Israel continues to launch air raids on civilians.
At least six Palestinians died Monday when Israeli F-16 fighter jets hit a series of targets, including Hamas-run al-Aqsa TV in Gaza City.
In retaliation, Hamas fired a barrage of rockets at Israel, including one that reached Ashkelon, killing an Israeli man in a home. Israel hit several densely populated areas that had both Hamas military and intelligence forces.
Palestinians also blew up an Israeli military bus as troops were exiting, injuring a 19-year-old soldier.
It's the worst escalation of violence since 2014.
Prime Minister Benjamin Netanyahu said Sunday he would do everything possible to avoid an "unnecessary war."
Hamas said in a statement the bus attack was a show of restraint because they could've inflicted more damage. The lone injured soldier was a message to Israel that, 'Look, we have the capability to inflict tremendous damage to you, but we do not want escalation,'" Ali Abunimah, co-founder of the Electronic Intifada website, told Al Jazeera.
Israel has reinforced its position at the Gaza border in anticipation of increased protests.
The violence came one day after a group of Israeli officers used a civilian vehicle to sneak into Gaza for an intelligence gathering mission. They killed a Hamas commander and fled with several Hamas fighters in pursuit. In all seven Palestinians and one Israeli officer died.