A 30-year-old Hamas affiliate was killed in the strikes, Gaza Health Ministry spokesperson Ashraf al-Qedra said. Several injuries were reported in several parts across the Strip. Israeli medics reported that four wounded people were taken to hospital.
Hamas has denied it launched the rocket at Beersheba, blaming a militant Salafi group in the strip instead.
US Envoy Jason Greenblatt who has been involved in peace negotiations between Israel and Palestine, pointed a finger squarely at Hamas for the escalation of violence.
Almost 160 Palestinians have been killed and some 17,500 others wounded in the fresh wave of violence, according to the latest figures released by the Palestinian Health Ministry.
According to the Israeli military, at least 11 rockets were intercepted by the Iron Dome aerial defense system, while a majority of the remaining rockets hit open areas.
On Wednesday, the Israeli military shelled the Palestinian territory after civilians working on the Gaza border fence came under fire.
The Ezzeddin al-Qassam Brigades, Hamas's armed wing, claimed responsibility for the rocket attacks, which came after two of its fighters were killed Tuesday by Israeli strikes inside Gaza.
Following May's rocket attacks, Israel and Gaza reached an uneasy cease-fire mediated by Egypt, though rocket launches and airstrike retaliation has continued.
It said the targets "included manufacturing facilities, training complexes and advanced weapons and capability sites" belonging to Hamas. "The exchange of fire continues, it's possible there will be a display of power - this time from our side - a few days of concentrated attacks, which will show Hamas the level of damage Israel can inflict if it insists on continuing".
Katz, meanwhile, proposed "shifting the full responsibility over the Gaza Strip to the global community, while keeping Israel's security control on the port".
It said Israel was targeted with around 150 rockets from late Wednesday into Thursday.
Israel and Hamas have fought three wars since the Islamic militant group seized control of Gaza in 2007.
Three Israelis were wounded by rocket shrapnel, while three Palestinians including a 23-year-old pregnant woman and her 18-month old child were killed in airstrikes.
Neither the United Nations nor Egypt has publicly discussed its plans for a renewed Gaza cease-fire, but they said it would bring economic relief to Gaza's 2 million residents experiencing shortages under crippling blockades.
The incident occurred while a group of senior Hamas leaders from overseas were visiting Gaza to discuss the ceasefire efforts with local leaders. "At this stage, we are considering evacuating settlements close to Gaza".
The gathering had raised hopes a deal for a lasting truce with Israel, with the backing of Egypt and the United Nations. "If current escalation however is not contained immediately, the situation can rapidly deteriorate with devastating consequences for all people". One Israeli soldier was killed by a Gaza sniper during this period.
Protests and clashes along the Gaza border since the end of March have seen at least 165 Palestinians killed by Israeli fire.