The UN's Mideast envoy appealed for calm.
The conflagration came as Egypt and UN-led efforts had been underway to reach a long-term ceasefire agreement between Israel and Hamas to bring to an end months of violence along the border and ease tensions in the impoverished Palestinian enclave.
Israel carries out regular attacks on Palestinians in Gaza under the pretext of hitting Hamas targets. Despite the animosity, the enemies appear to be working through Egyptian mediators to avoid another war.
Wednesday's exchange came just a day after two members of the Gaza Strip's ruling Hamas movement were killed by Israeli fire. A statement from the military wing of Hamas claimed responsibility for the rockets.
In response to the rocket fire, the Israeli Air Force bombed 12 Hamas targets in Gaza.
The escalation comes after the Hamas leadership convened for a rare meeting in Gaza on Friday.
Despite the escalation between the two sides, The Associated Press quotes an unnamed Hamas official as saying that cease-fire talks were in their final stage even though disagreements persisted.
At least two Palestinians were wounded in raids aimed targeting a Hamas base in the southern Gaza Strip, the enclave's health ministry said. According to Professor Yochanan Pfizer, deputy director of Soroka Medical Center, said that the injured woman was suffering from shrapnel wounds to her stomach.
The mother and daughter died immediately and the father is in critical condition, Kamal said.
Israel has been battling large fires caused by kites and balloons rigged with incendiary devices or burning rags launched from Gaza that have destroyed forests, burned crops and killed wildlife and livestock.
On Tuesday, Israel struck a Hamas military post in Gaza, saying it was in response to militant fire at Israeli troops. Israeli medics reported that four wounded people were taken to hospital.
Thirty of rockets were intercepted by the Iron Dome missile defense system, which is activated only against those projected to hit populated areas, whilst the majority of the projectiles fell in open areas.
"As of now, 36 rocket launches were identified from Gaza towards Israel", the army tweeted. "We are reinforcing the southern command and Gaza division".
Sirens sounded in Israeli areas near Gaza, warning residents to seek immediate shelter, the Israeli army said.
Jewish community representatives complained to the broadcaster after an initial headline read "Israeli air strikes 'kill woman and toddler'".
"We have had another night of escalation and we are not seeing the end", he said.
Israel says it is defending its border and nearby communities and accuses Hamas of using the protests as cover for attempts to breach the fence and carry out attacks. The protests have been aimed in part at trying to break the blockade.
They were killed in an airstrike in Jafarawi in central Gaza, the ministry said, while her husband was injured.
One Israeli soldier has been shot dead by a Palestinian sniper. Our strong commitment to the State of Israel's right to defend its borders and civilians is uncompromising.