"It is time for the Muslim ... to unite for the sake of Jerusalem and Palestine after the Jews have increased the corruption in the world, and shed the blood of (Muslims)," Badie said. The comments were denounced as hate speech by organizations that track anti-Semitism.
Peace talks between the Israelis and Palestinians have stalled over Israel's refusal to stop Jewish settlements in the West Bank, which Palestinians claim as their future state.
Gamal Soltan, a political science professor at the American university in Cairo, said the Brotherhood may be playing to a regional audience in evoking the Palestinian crisis.
"Morsi as president, trying to act as a statesman, is responsible for running the country. Badie has more freedom to express views," Soltan said.
Israeli lawmaker Danny Danon called on the United States and the European Union to take action, adding that such "incitement and anti-Semitism in Egypt" must stop before Washington sends more financial aid to Cairo.
"The direction of the new Egyptian government is very worrying and we are following with great concern what is being said and done and what is not being done there against extremists," he said in a telephone interview Saturday.
Brotherhood spokesman Mahmoud Ghozlan said Israel's suspected possession of nuclear weapons coupled with wars in the Gaza Strip and Lebanon and "the slaughter of Palestinians and expansion of settlements" means that relations with Egypt cannot be "normal."
Ghozlan insisted the Egyptians would adhere to the terms of the 1979 treaty, "but we are dealing with Israel at the limits of the treaty.
"Improved relations were with the former regime ... against the will of the people, the will of Arab people and the will of Palestinians. Now relations are different."
Beyond religious links to Jerusalem, the Brotherhood inspired the formation of Islamic militant groups around the Middle East, including the Palestinian Hamas. Badie, who was once part of a group of radical members charged with seeking to overthrow Egypt's government, has since renounced violence, but supports Hamas in its "resistance" against Israel and met with Hamas premier Ismail Haniyeh last year in Cairo.
Soltan, the political science professor, warned that the Brotherhood and Morsi cannot continue this "duality" for long.
"They continue to be torn apart between ideology on the one hand and politics on the other," he said. "To survive as a president for Egypt he has to pursue a moderate policy vis-a-vis Israel and there will definitely be people in the Brotherhood who don't like that."
Associated Press correspondents Sarah El Deeb in Cairo and Diaa Hadid in Jerusalem contributed to this report.