Palestinian militants responded with heavy fire on southern Israel, launching almost 400 mortar rounds and rockets that wounded 27 people and killed one - a Palestinian living in southern Israel. Daoud Shehab, a spokesman for the Islamic Jihad militant group, said each side would promise quiet in exchange for quiet.
The Cabinet said it had ordered the military to "continue operations as needed".
At a demonstration staged in the rubble of Hamas' TV station, demolished by an Israeli airstrike, crowds chanted the name of Hamas' military wing.
Hamas accused Israel of "deliberate targeting of civilians and civilian facilities" in one of the most densely populated places in the world.
Rocket attacks from Gaza sent residents of southern Israel to shelters, wounding dozens and killing a Palestinian labourer from the occupied West Bank.
Palestinians check on Tuesday the damage of a building destroyed by Israeli airstrikes in Gaza City.
Mansour, who spoke to reporters well after Danon had left, blamed the IDF's botched Gaza operation for the violence. The statement thanked "the efforts of Egypt, Qatar, Norway, and United Nations exerted to stop the Israeli attack".
In 2010, the US Treasury listed Al-Aqsa TV as a specially designated global terrorist.
"Egypt's efforts have been able to achieve a ceasefire between the resistance and the Zionist enemy", the statement by the Gaza groups said.
Egypt has negotiated ceasefires following previous flare-ups, while UN Middle East envoy Nickolay Mladenov has also been seeking a long-term truce in recent weeks. "Rockets must STOP, restraint must be shown by all!" he wrote on Twitter.
"This is happening at a delicate juncture in Hamas-Israeli relations", Hugh Lovatt, a regional expert at the European Council on Foreign Relations, told DW. "This will severely harm our security in the long term", Lieberman added.
Hamas armed wing accused Israeli forces on Sunday of having "infiltrated this evening in a civilian car" and assassinating a top commander.
The deal has provoked criticism from within Netanyahu's government as well as from Israelis who live near the Gaza Strip and want further action against its rulers Hamas.
Meanwhile, Israel okayed Qatar's initiative to transfer funds to Hamas officials in Gaza and cover their salaries for six months in a bid to prevent a humanitarian crisis in the region.
Violence has simmered since Palestinians launched weekly border protests on March 30 to demand the easing of the blockade and the right to return to land lost in the 1948 war of Israel's founding.
The violence saw seven Gazans killed in 24 hours as Israeli strikes targeted militants and flattened buildings, sending fireballs and plumes of smoke into the sky.
Officials in Bayit Yehudi (The Jewish Home), a party that has eight seats in the Knesset, warned that they will pull out of the coalition if their chairman Naftali Bennett, who now serves as Education Minister, replaces Liberman.
Speaking at a press conference in Israel today, Lieberman began by saying that "I assume everyone has tried to guess and I think you guessed correctly - I am indeed here in order to resign from my position as defence minister".