Militants fired 300 rockets and mortars at Israel. One hit an empty bus, seriously injuring a soldier nearby.
Israel responded with more than 70 strikes on what it said were targets belonging to Hamas and Islamic Jihad.
Three Palestinians, two of them reportedly militants, were killed.
The Hamas-run health ministry in Gaza said nine Palestinians were injured.
Meanwhile, Israeli medics said 10 people in Israel were injured.
Israeli Maj Gen Kamil Abu Rukun warned that Hamas "has crossed a red line" and Israel would "continue to respond with an iron fist against all terrorist activity or rocket fire"".
Israeli Prime Minister Benjamin Netanyahu cut short his visit to France for an urgent meeting with his security chiefs.
A Hamas commander and an Israeli soldier were among the dead on Sunday.
Palestinians said an Israeli unit travelling in a civilian vehicle had killed the Hamas commander.
According to Palestinian sources, the Israeli unit was about 3km (2 miles) inside the Gaza Strip, which borders Israel, when militants from Hamas, which controls the Gaza Strip, stopped the car.
The group's military wing, the Izzedine al-Qassam Brigades, said the Israelis opened fire, killing a local commander, Nur Barakeh.
The incident is reported to have happened east of Khan Younis, in the south of the territory.
A gun battle erupted and Israeli tanks and aircraft opened fire in the area, witnesses said.
Six of the Palestinians killed belonged to Hamas and the seventh was a member of the militant Popular Resistance Committees, AFP news agency cited Palestinian officials as saying.
The Israel Defense Forces (IDF) said a member of the special unit involved was killed and another was lightly wounded.
The Israeli soldiers were later flown back by helicopter.