One Israeli soldier was killed by a Gaza sniper during this period.
One Hamas militant was killed in the air strikes, as was a Palestinian woman and her 18 month old child, Palestinian officials 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.
It further claimed that the Israeli missile system Iron Dome had intercepted 25 rockets out of the 150 rockets, which activated sirens in the occupied territories over 125 times.
Israel's rescue service Magen David Adom said three Israelis, including two men aged 34 and 20 were taken to hospital for treatment.
More than 100 rockets have been fired into Israel since yesterday from the Gaza strip.
A senior IDF official asserted Thursday morning that the escalation in the south might lead to a broad campaign in Gaza which would the evacuation of communities along the border.
The Gaza Health Ministry said that a Hamas fighter and the two civilians were killed in separate incidents.
Eight others were also injured in the attacks, the ministry said in a statement.
Israeli army spokesman Lt. Col. Jonathan Conricus insisted Israel only targeted Hamas military targets in Gaza.
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Israel and militants in Gaza have exchanged frequent fire in recent months. That was followed by the rocket fire and then the Israeli strikes.
Residents of Israeli communities near the Gaza border were instructed on Wednesday night to remain near protected spaces.
Yuval Steinitz, a member of Prime Minister Benjamin Netanyahu's inner cabinet, told Israel Radio before the Palestinian officials comments that Israel was "not eager for war" but would make no concessions to Hamas. However, Israel appears to be learning more towards a quid-pro-quo agreement with Hamas instead of a comprehensive ceasefire, as past resolutions have often crumbled.
On Wednesday, UN Middle East envoy Nickolay Mladenov condemned the Hamas rocket fire and called for both sides to step away from the brink.
A number of Israeli homes, factories, schools and playgrounds were hit during the barrage.
The nearly daily airborne arson attacks have been part of months of weekly border protests led by the Islamic militant group Hamas that rules Gaza aimed in part at drawing attention to the Israeli-Egyptian blockade imposed after it took control of the territory in 2007.
The attacks come as the United Nations and Egypt try to secure a deal between Israel and Hamas for a lasting truce. "What is required is for calm to be restored along the border between us and the Zionist enemy".
It was the third severe flare-up of violence since July and came despite attempts by United Nations officials and Egypt to secure a long-term truce between Israel and Hamas.
This was the first attack directed against the city since the 2014 war, known in Israel as Operation Protective Edge.