Ayelet Shaked told local radio on Tuesday that Israel could overrun the Palestinian enclave in relation to the largest projectile barrage from Gaza targeting Israel since a 2014 war.
"We must prepare to occupy Gaza as a part of efforts to eliminate Hamas rule," Shaked said, according to a translation by Palestinian-Israeli news website Arab48.
Commenting on the projectiles fired towards Israel earlier in the day, she said: "a disaster could have happened that led to war".
"The response must be very severe, as if blood has been spilled here. All options are on the table, including occupying the Gaza Strip," the minister added.
The Israeli military said on Tuesday that it struck more than 30 "military targets" in the Gaza Strip after mortar shells and rockets were fired at Israel.
The majority of some 28 projectiles were intercepted by Israeli air defences and no injuries were reported.
Later in the day, Israel said it intercepted further projectiles fired from the Gaza Strip.
There was no immediate claim of responsibility, but there was speculation the mortars were fired by Islamic Jihad in revenge for a recent incident that left three of its members dead.
Hamas, the Islamist movement that runs the Gaza Strip, said in a statement "what the resistance carried out this morning comes within the framework of the natural right to defend our people".
Tuesday's incidents follow the Israeli massacres of Palestinian protesters along the Gaza border that started on March 30.
They peaked on May 14, when at least 61 Palestinians were killed as tens of thousands of Gazans protested on the same day of the US transfer of its embassy in Israel from Tel Aviv to Jerusalem.
At least 116 Palestinians have been killed by Israeli fire and more than 10,000 have been injured since mass demonstrations began on March 30.
No Israelis have been killed and only a few soldiers have suffered minor injuries.
The protests - dubbed "Great Return March" - have centred on the right of Palestinian refugees to return to their homes, after they were expelled following the 1948 creation of Israel.
Protesters have also demonstrated against the crippling decade-long Israeli blockade of the Gaza Strip.
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