The Kerem Shalom border crossing is one of the two border crossings between Israel and the Gaza Strip.
When Israel finishes dealing with Hamas, the interests of Israel and those of Hezbollah and Iran will likely align, for a short time, to postpone the wider fighting in the north.
The rockets were reportedly launched from the Rafah area. The Kerem Shalom crossing was closed after the attack.
The target of Israel's ire was UNRWA, the UN agency that Israel has called on nations to defund.
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The protests have occurred for several months. Early in February, dozens of protesters blocked the path of humanitarian aid trucks to Gaza also at the Kerem Shalom crossing.
The crossing has been closed since 2011.
Ben-Gvir took aim at the military chief for the IDF's cooperation with Israel Police in foiling daily protests against the delivery of humanitarian aid into Gaza.
The protests continue as Israel explores new ways to provide humanitarian aid to Hamas instead of through UNRWA.
Among the organizers of the protests is the Tikvah Forum, a group composed of families of Israeli hostages who favor a more hardline response to Hamas.