A 30-year-old Hamas affiliate was killed in the strikes, Gaza Health Ministry spokesperson Ashraf al-Qedra said.
The flare-up came after officials on both sides had talked about potential progress in U.N and Egyptian efforts to broker a truce to end months of simmering violence.
Hamas has denied it launched the rocket at Beersheba, blaming a militant Salafi group in the strip instead.
More than 160 Palestinians have been killed by Israeli forces - most during weekly protests at which thousands of Palestinians have expressed their support for the declared right of Palestinian refugees to return to their ancestral homes in what is now Israel.
On Thursday, hours before the Palestinian official announced that the violence had ended, a senior Israeli military official said that the army was "nearing war with Gaza" and would evacuate Israelis living in communities adjacent to the border if necessary.
What outraged the Israeli side is the BBC's "deliberate lying", while not mentioning the fact that the Israeli bombing was triggered by the rockets fired from Gaza toward southern Israel as the Israeli media reported, despite Hamas' denial.
"After bringing it to the BBC" s attention, the headline was altered to read "Gaza air strikes "kill woman and child" after rockets hit Israel".
Hamas's military wing said it was behind the rocket attacks.
A pregnant woman and her one-year-old daughter were among three people killed during Israeli air strikes along the Gaza Strip.
Some source reported that were spotted IDF's tank and heave armored vehicles that heading toward Gaza border as serious escalations occur tonight.
The Israeli Air Force (IAF) responded by attacking over 150 Hamas terror targets throughout the Strip, including a cement factory used by Hamas to build terror tunnels, a maritime terror tunnel shaft, a weapons manufacturing and storage facility, and several terror sites in military compounds.
Both the United Nations and Egypt have not publicly discussed their plans for a renewed Gaza ceasefire, but have said it would bring economic relief to Gaza's two million residents experiencing shortages under crippling blockades.
Israel carries out regular attacks on Palestinians in Gaza under the pretext of hitting Hamas targets.
Hamas claimed responsibility for the mortar barrage, saying it came in response to the IDF's killing of its two operatives on Tuesday.
On Wednesday, Israeli Prime Minister Benjamin Netanyahu convened an emergency meeting of his security Cabinet - which includes Defense Minister Avigdor Liberman and senior army commanders - to discuss mounting tensions along the Gaza-Israel buffer zone. "If current escalation however is not contained immediately, the situation can rapidly deteriorate with devastating consequences for all people".
The statistics showed that 155 Palestinians were shot and killed, while 17,259 suffered from various injuries, including tear-gas suffocation.
"We can say that actions led by the United Nations and Egypt are in advanced stages and we hope it could yield some good from them", Khalil Al-Hayya, deputy Hamas chief in Gaza, told Al Jazeera television.