10:36AM EST November 16. 2012 - CAIRO – Thousands of Egyptians took to the streets Friday protesting Israeli attacks on the Gaza Strip, waving Palestinian flags across the Egyptian capital and demanding the Egyptian government cut ties with Israel.

"We're here today to say to Israel: Go to Hell," said Mustafa Kamel from a Cairo neighborhood called Imbaba at a demonstration outside Al-Azhar Mosque that was planned by the Muslim Brotherhood. "Muslims are strong. In Egypt, we refuse Israel and the politics of America."

Demonstrations also took place in Tahrir Square following days of intense escalation in violence between Israel and the Gaza Strip, posing challenges for Egypt's new government and its president, Mohamed Morsi.

"The Muslim Brotherhood has made it clear they want to use this as an excuse to sever ties," said Eric Trager of the pro-Israeli Washington Institute for Near East Policy.

Morsi,who formerly headed the Brotherhood's political wing but no longer officially belongs to the party, is caught between his ideology and affiliation with the group and the Egyptian officials he's entrusted to manage Egypt-Israel relations, Trager said.

The matter of ties between the two nations is a "sensitive issue" for Morsi, said Mohamed El Mekkawi, a member of the foreign relations committee for the Brotherhood's Freedom and Justice Party. The Egyptian president has tried to create a new strategy for relations based on the pillar of benefits between Egypt and Israel, but Israeli attacks on Gaza have "complicated the situation,"he said.

The border area was calm Friday as Hamas, which controls the Gaza Strip. met with diplomats from Egypt and Turkey. Hamas is a designated Palestinian terror organization and has fired hundreds of rockets into Israeli neighborhoods this year. Last weekend Hamas terrorists fired nearly 200 rockets in a barrage that Israel vowed to stop.

The Palestinians say at least 19 people have been killed by the Israeli attacks. Israel said that is regrettable but that it is Hamas that bears responsibility for the deaths by its unprovoked attacks on Israeli civilians.This week Israel launched with air attacks against various targets inside Gaza: weapons depots and rocket factories. On Wednesday it fired a missile into the car containing a Hamas military commander, killing him.

On Thursday, a rocket from Gaza aimed at a neighborhood in southern Israel killed three people in their apartment, including a pregnant mother of two.

After months of speculation about how an Islamist-led government would deal with its neighbor, the escalating crisis between Israel and Gaza may indicate if Morsi will do what Hosni Mubarak didn't: Recalibrate relations with Israel without doing damage to Egyptian interests, or convincingly explain to the Egyptian public why he isn't changing his policies and then get away with it, said Hussein Ibish, a senior fellow at the American Task Force on Palestine in Washington.

The most logical path for Morsi, however, is to reflect Mubarak's actions and be the one interlocutor who can talk to Hamas without enhancing their diplomatic standing, Ibish said. Egypt's Prime Minister Hesham Qandil visited Gaza Friday morning to show solidarity with Palestinians and said Cairo would try to foster a ceasefire.

"If he can try to do that, and if he does do that, it will be a pretty neat escape from a nice little trap that's been set for him," Ibish said. "It depends a lot on how this is perceived in Egypt, how Morsi explains his policies to the Egyptians, and how the Egyptians understand relations between emotions and national interests."

Whether the Egpytian military would approve of any action against Israel is questionable. Morsi has exerted some influence over the military but it remains a powerful and independent force in Egyptian politics that has maintained a peaceful relationship with Israel for decades under Mubarak.

But different from Mubarak, Morsi rose to power in a democratic election and is expected to cater more to the demands of the Egyptian street and less to those of Western powers.

"Where are the human rights with what happened in Israel?" asked Mohammed Gouma, 22, a protester from Beni Suef. "Children are being killed in Gaza, and what has Barack Obama done?"

Obama said Thursday that Israel has the right to defend itself.

Morsi said Thursday in a televised speech that Israel's attacks on Gaza were "unacceptable"and that they threatened to destabilize the region. For months, the region has already been on edge over growing militancy in Egypt's Sinai Peninsula, which shares a border with Israel and has been a base for attacks on the Jewish nation.

On Wednesday, Egypt withdrew its ambassador from Israel and Morsi later called for an urgent meeting of the Arab League.

"He's been, as usual, more creative than observers originally anticipated," Trager said. "Recalling his ambassador, that's a light move – something Mubarak did."

Sending the prime minister to Gaza, however, is very bold, he said. While the visit doesn't have a direct consequence for Egypt-Israel relations, it demonstrates strong support for Hamas. Some on Friday still demanded more from Morsi.

"We want him to alter the Camp David agreements and cut relations between Egypt and Israel," said Hossam Mohammad Anter, a teacher from the Nile Delta.

But Anter concedes that presently, this may not be in Egypt's best interest.

"Egypt is not strong enough to make war with Israel," Anter said. "So, we'll have to go step by step."