The ministry said three people, including a pregnant woman, were killed in northern Gaza and two in southern Gaza, raising an earlier toll of seven.
On Thursday, Israel said its aircraft struck a Hamas military compound after balloons carrying firebombs and explosives were launched across the border.
The Erez crossing for people and the Kerem Shalom crossing for goods reopened Sunday morning, a spokeswoman for COGAT, the defence ministry unit that oversees the crossings, told the media.
Israel's army had earlier reported a rocket fired from the Gaza Strip at Israel but a spokeswoman could not comment further for now.
The zoo in the war-battered Palestinian enclave is promoting itself as offering the chance to play with the 14-month-old declawed lioness, which is supposed to be placid enough to meet visitors.
The raids were done after the Israeli army struck on two Hamas posts on Sunday after balloons carried an explosive device over the border fence.
The Israeli military said its aircraft had fired towards a militant who was part of a group launching projectiles at its territory, without confirming the death.
The armed wing of Hamas threatened to step up its attacks and fire rockets further north toward the Israeli cities of Ashdod and Beersheba if Israel continued its airstrikes.
Netanyahu made the comments in a briefing to local journalists on Monday, various Israeli newspapers reported.
Two other Palestinians were killed in other protest locations, the ministry said, adding that at least 140 Palestinians were wounded by live bullets.
Egyptian and United Nations officials have been mediating indirect negotiations on a long-term truce between Israel and Gaza's Islamist rulers Hamas, who have fought three wars since 2008.
Army spokesman Jonathan Conricus told journalists the rocket and mortar fire at Israel was the most extensive since a 2014 war as was Israel's response.
Eyewitnesses said after Friday prayers, hundreds headed to five different locations along the border. Israeli soldiers using loudspeakers warned the demonstrators, asking them to "Go home for your saf
The court, however, removed Sri Lanka's Liberation Tigers of Tamil Eelam from the 28-member bloc's terror list, BBC reported.