Prime Minister Benjamin Netanyahu visited a southern Israeli town bordering Gaza on Tuesday that was pummeled with rockets from the strip over the weekend and told community leaders there that Israel is engaged in a "lengthy battle".
The legislation has been dubbed the "Breaking the Silence" law, a reference to the Israeli group of that name which collects and publishes testimony from Israeli veterans about the military's treatment of Palestinians in the occupied West Bank and during conflicts with militants in Gaza.
Later, Mr Lieberman announced that Kerem Shalom would be closed for fuel deliveries and the distance which Gaza's fishermen would be allowed from the coast reduced from six nautical miles (12 km) to three.
Israel has tightened restrictions on its only cargo crossing with the Gaza Strip, after Palestinians carried out fresh attacks with incendiary balloons.
According to Palestinian media reports, Israel also deployed three drones to strike Palestinians launching incendiary kites and balloons, wounding three terrorists.
With Israel focused on efforts to prevent Iran from establishing a permanent military foothold in neighboring Syria, it has been wary of escalating violence in Gaza.
It comes days after Israel suspended imports and exports through the crossing except for basic humanitarian supplies - fuel, food, some medical equipment and medicine, livestock, and animal feed - in order to put pressure on Hamas.
Hamas, which dominates Gaza, warned Israel of "dangerous consequences".
Kanou called on the global community to "break its silence towards Israeli crimes against humanity".
Later in the day, Israel said a projectile - possibly a rocket - was sacked from the Gaza Strip but appeared to have fallen within the Palestinian enclave.
"The focus of the attack is a wide-scale strike of the Hamas Battalion HQ in Beit Lahia, which includes urban warfare training facilities, weapon storage warehouse, training compounds, command centers, offices, and more", the IDF said in a statement.
Citing the daily Hebrew-language newspaper Israel Hayom, IPT said Hamas is preparing to mount explosive material on unmanned aerial vehicles to target Israel communities deeper into the country.
The European Union also criticized the restrictions, saying it "expects Israel to reverse these decisions" which risked "further aggravating the already dire economic situation in Gaza".
More than 130 Palestinians have been killed by Israeli forces in the protests.
Israel says its use of live fire is necessary to defend its borders and stop infiltrations.