Militants in the Gaza Strip have fired more than 200 rockets into Israel, the army says, prompting air strikes and tank fire on the Palestinian territory.
Three Israelis were wounded by the rockets. Israeli fire killed three Palestinians, including a mother and her baby daughter, Gaza officials say.
Four Palestinians, including two Hamas militants, were killed on Friday after an attack injured two Israeli soldiers.
The flare-up followed a truce in the run-up to Israeli elections in April.
It marks yet another increase in hostilities despite attempts by Egypt and the United Nations to broker a longer-term ceasefire, says the BBC's Tom Bateman in Jerusalem.
What happened on Saturday?
The rocket barrage hit several homes in parts of Israel bordering the Gaza Strip. Many residents rushed to bomb shelters.
The injured include two men in Ashkelon, 10km (six miles) north of Gaza, and an elderly woman in Kiryat Gat, further east.
The country's Iron Dome missile-defence system shot down dozens of the rockets, the Israel Defense Forces (IDF) said.
In response the IDF launched air and artillery strikes against 30 Gaza sites belonging to Hamas, a militant group that controls the Gaza Strip, and against groups including Islamic Jihad. It blamed both for the attacks.
Palestinian officials say a 22-year-old man was killed. Reuters news agency quotes a small pro-Hamas militant group as saying he was one of their fighters.
The other death was that of a woman and her 14-month-old daughter who were killed in an air strike in the east of the Gaza Strip, according to Palestinian officials.
Several Gaza residents were wounded.
Islamic Jihad said it had launched the rocket attacks in response to Friday's violence.
The statement also accused Israel of failing to implement last month's ceasefire deal, which was brokered by Egypt.
What triggered the latest unrest?
The violence began during weekly Friday protests in Gaza against the tight blockade of the area. Israel says this is needed to stop weapons reaching Gaza.
A Palestinian gunman shot and wounded two Israeli soldiers at the boundary fence. The IDF blamed Islamic Jihad for the shooting.
The Israeli air strike in response killed two Hamas militants. Another two Palestinians were killed by Israeli fire at the fence.
Saturday's rocket attacks coincided with Palestinians burying the two militants.
Israel says it has targeted militant sites in Gaza - this one is in Gaza City
"The resistance will continue to respond to the crimes by the occupation and it will not allow it to shed the blood of our people," Hamas spokesman Abdel-Latif al-Qanoua said in a statement on Saturday. He made no explicit claim for Hamas firing the rockets.
About two million Palestinians live in Gaza, which has suffered economically from the Israeli blockade as well as recent foreign aid cuts.