In a statement, the Isreali military said fighter jets, attack helicopters and tanks hit Hamas underground infrastructure and military posts.
At least two rockets were fired from the Gaza Strip the previous evening, one of which was intercepted by Israel's Iron Dome anti-missile system.
Hamas is pressing Israel to ease its blockade on Gaza and allow large-scale development projects. Egypt and Qatar are trying to shore up an informal cease-fire.
Israel and Egypt imposed a crippling blockade on Gaza after Hamas seized power from rival Palestinian forces in 2007.
The Health Ministry says the deceased was a 61-year-old man who had been put on life support and died during his transfer to a special isolation center.
The army said in a statement that it bombed “military posts and an underground infrastructure” belonging to the Hamas militant group that rules the Palestinian enclave.
There were no immediate reports of casualties or major damage.
Protesters burned Israeli and American flags, trampled on posters of Israeli Prime Minister Benjamin Netanyahu and President Donald Trump.
The strikes came as visiting Egyptian security officials strove to defuse the latest uptick in violence, a Hamas source said.
Israeli fire services in the border areas reported 28 outdoor fires Sunday, and farmers said that extensive damage was caused to an avocado orchard.
Palestinian militants in Gaza fired two rockets into southern Israel after Israeli airstrikes targeted sites belonging to the territory's militant Hamas rulers.
The strikes followed successive rounds of cross-border fire from Gaza on Friday and the launch of balloons fitted with incendiary devices into southern Israel.
It came a day after the United States transferred its Israel embassy from Tel Aviv to the disputed city of Jerusalem in a move that infuriated the Palestinians and was widely condemned.
The UN rights office said Tuesday it seemed any Palestinian protesting in Gaza, regardless of whether or not they posed an imminent threat, was "liable" to be killed by Israeli forces.
The U.N. Security Council planned to meet Tuesday to discuss the violence, though it was not clear what might come out of the session.