Injuries were also reported on both sides.
A Palestinian was killed in northern Gaza, while at least six were wounded in raids aimed targeting sites across the strip, the Gazan health ministry said.
Hamas, the Islamist group that runs the Strip, named the dead man as Ali Ghandour, saying he was a member of the group's armed wing.
The strikes came after at least two of dozens of rockets launched from the coastal enclave hit the Israeli town of Sderot, near Gaza's northern border, police and the army said.
One person was lightly wounded by shrapnel while several others were treated for shock in Sderot, the United Hatzalah medical service said.
A statement from the military wing of Hamas, the Islamist group that runs Gaza, claimed responsibility for the rockets. It said the Palestinian "resistance" had fired a large number of rockets at "enemy positions in the Gaza envelope." Sirens were sounded in several Israeli areas close to the border with Gaza, warning residents to seek immediate shelter, the Israeli army said.
The majority hit open areas while 11 were intercepted, it said.
Israeli television broadcast images of a house and cars reportedly damaged by the rockets in Sderot. Parts of the town have been closed off and police bomb disposal units were at the scene of the strikes, a spokesman for the force said.
"I am deeply alarmed by the recent escalation of violence between Gaza and Israel, and particularly by today's multiple rockets fired towards communities in southern Israel," UN envoy Nickolay Mladenov said in a statement.
He called on all sides to step "back from the brink." The strikes came after two fighters from the military wing of Hamas, which rules Gaza, were killed by Israeli fire on Tuesday.
The escalation comes after the Hamas leadership convened for a rare meeting in Gaza on Friday.
The gathering had raised hopes a deal for a lasting truce with Israel, with the backing of Egypt and the United Nations. Clashes along the Gaza border since the end of March have seen at least 163 Palestinians killed by Israeli fire.
One Israeli soldier has been shot dead by a Palestinian sniper.
Israel and Hamas have fought three wars since 2008.
The last war in 2014 ended with a tense ceasefire and analysts say another round of conflict remains likely.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)