The Israel Defense Forces said the attack was in response to a shooting attack carried out against its soldiers earlier in the day as Palestinian protesters gathered along the fence that separates Israel and Gaza.
More than 135 mostly unarmed Palestinians have been killed by Israeli fire since the border protests began on March 30.
Successive explosions rocked Gaza City at nightfall and streets emptied as warplanes struck sites that Israel said belonged to the military wing of Hamas, the Islamist group that controls Gaza.
On Saturday, Israel pounded Hamas targets in its largest bombardment campaign since the 2014 war, as Gaza militants fired dozens of rockets toward Israel. "Hamas chose to deteriorate the security situation and will bear the responsibility for its actions", the IDF said in a statement. Gaza's ministry of health said that other people were injured.
At least four Palestinians were killed in later Israeli strikes, according to Palestinian medical officials.
The violence came during another Friday of protests by Palestinians at the border between Israel and the Gaza strip.
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Hamas on Friday vowed it will continue weekly protests and the launching of incendiary devices at Israel.
Israel and Hamas later agreed to restore calm along the Gaza Strip following the flare-up which lasted several hours.
The United Nations envoy for the Middle East peace process, Nickolay Mladenov, said on Twitter that "everyone in Gaza needs to step back from the brink". "Right NOW! Those who want to provoke Palestinians and Israelis into another war must not succeed".
Israel's Prime Minister Benjamin Netanyahu met with Army Chief of Staff Lt. Gen Gadi Eizenkot and Mr. Lieberman at the military's headquarters in Tel Aviv to discuss the escalating tensions in Gaza.
Since March, Palestinians have regularly protested at the fence dividing Gaza from Israel-calling for an end to Israel's blockade and to be allowed to return to the land from which they fled during the 1948 war with Israel.
Lieberman has raised the threat of a large-scale operation in the Gaza Strip if Hamas does not stop the kites and balloons being launched.