The powerful group said in a statement that "the Egyptian government must be the first to (cut ties), and serve as an example to Arabs and Muslims who maintain relations with this entity."
The statement further called on the Palestinian Authority to immediately halt its defense cooperation with the IDF.
The Brotherhood urged Egyptians to take to the streets and protest in front of major mosques in Cairo and other cities after Friday prayers, with a central rally taking place in front of the Al-Azhar Mosque in the capital.
The demonstrations are meant to show that Egyptians denounce the Israeli strikes on Gaza.
"We urge the entire nation to join the Muslim Brotherhood in showing our rage over the Zionist entity's attacks and our support for the Palestinian resistance at rallies that will take place after Friday prayers," Muhammad Badie, the movement's supreme guide, said on Facebook.
Cairo 'negotiating lull'
Meanwhile, an Egyptian defense official told the Alquds Alarabi newspaper that the Israeli operation in Gaza is expected to last several days. "Cairo will continue negotiating with Israel in an effort to halt the attacks," he said.
More than 110 rockets were fired at Israel since the beginning of Operation Pillar of Defense, which was launched Wednesday. The operation led to the death of Al-Jabari, as well as several other terrorists.
Meanwhile, the IDF continued to strike Gaza and hit several terrorist targets including rocket launching sites. The Palestinians reported that three people were killed in a strike on Khan Younis early on Thursday.
Also Thursday, a United Nations Security Council emergency meeting on Operation Pillar of Defense ended after 90 minutes without any resolution.
During the meeting, held at the request of Egypt, Morocco and the Palestinians, the representatives of the 15 member states were briefed on the developments by Under Secretary General for Political Affairs Jeffrey Feltman.
The Palestinian Authority's UN envoy, Riyad Mansour, told the Security Council, "Once again the international community is witness to Israel's malicious onslaught, using the most lethal military means and illegal measures against the defenseless Palestinian civilian population."
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