One Israeli soldier has been shot dead by a Palestinian sniper during the same period, while incendiary devices attached to balloons and kites launched by Palestinians have sparked hundreds of fires in southern Israel, burning some 3,000 hectares (7,400 acres) of forest and farmland.
Israeli television broadcast images of damage to homes and cars in the town of Sderot.
Israel's military says it struck several Hamas targets in Gaza.
Earlier on Wednesday, before the rocket fire, a Hamas official said these negotiations were in "advanced stages".
Jason Greenblatt, a United States envoy who has been involved in peace negotiations between Israel and the Palestinians, pointed a finger squarely at Hamas for the escalation of violence.
Israel's rescue service Magen David Adom said three Israelis, including two men ages 34 and 20, were taken to a hospital for treatment.
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.
The incident occurred while a group of senior Hamas leaders from overseas were visiting Gaza to discuss the ceasefire efforts with local leaders.
Presumed American remains from Korea War head home
They set the caskets gently on risers lined up inside the hangar as Mr Pence stood watching with his hand over his heart. Critics say the summit has so far failed to deliver on promised steps toward denuclearisation by Pyongyang.
A fireball exploding during Israeli air strikes in Gaza City. Iron dome intercepted 28 rockets and most of the others fell on open ground but there was a direct hit on a house in the Hof Ashkelon region and injuries in Sderot and the Eshkol region.
In that incident, two fighters from the military wing of Hamas were killed by Israeli fire along the border.
Get ready, or not: An army official's warning that a war with Gaza is a very real possibility and southerners should get ready to evacuate the Gaza border region may have been meant as a scare tactic in the hopes that Hamas will realize how sideways things are about to turn, but that doesn't mean it's not also true.
Responding to the spate of violence overnight, president of the Board of Deputies of British Jews, Marie van der Zyl said she is "deeply concerned about the escalation of violence and the more than 150 rockets fired at Israel. If the current escalation is not contained immediately, the situation can rapidly deteriorate with devastating consequences for all people".
On Thursday, the IDF destroyed a five-story building allegedly housing Hamas' internal security service and offices of the group's senior officials.in response to a rocket fired at Beersheba, almost 40km from the border with Gaza.
Protests and clashes along the Gaza border since the end of March have seen at least 165 Palestinians killed by Israeli fire.
After a few hours of relative quiet, Israeli forces targeted western Gaza City on Thursday evening, the Gaza health ministry reported, adding that at least seven Palestinians were injured.
The video was also shared by at least one account in Gaza as proof that Hamas should not be messed with and will hit back if attacked.