As the death toll in Gaza passed 500 on Monday, regional peacemaker Egypt and Hamas play ideological politics.

Both the Egypt government and Egyptians were once strong supporters of the Palestinian cause, but that relationship soured largely thanks to Hamas’ traditional ties to the Muslim Brotherhood. Complicating the matter are provocations from Egypt such as the judicial ban laid on Hamas in March and the diplomatic presence of Qatar and Turkey, both of which supported the Muslim Brotherhood government of ousted president Mohamed Morsi. At stake is a ceasefire to end the rapidly rising toll of civilian death and injury, yet one side refuses to use the other’s name, and the other is split between moderates and those in charge of Gaza.

The Egyptian government does not refer to Hamas by name in its press releases, and foreign ministry spokesman Badr Abdel Atty couldn’t bring himself to say the word during a phone interview. In response to questions about whether the Egypt government was speaking directly to the faction, he answered: “We are speaking with all Palestinian factions without exception … Again I’m sticking to what I said, again, we are talking we have been in consultations with all Palestinian factions before and after issuing the initiative.”

Those factions include Islamic Jihad and the Democratic Front for the Liberation of Palestine, but in the main Egypt negotiates with the Palestinian Authority. This is especially so given the Unity Government deal struck between the Gaza and West Bank leaderships after the failure of United States-backed peace talks in April.

Atty repeated that Egypt was working with all factions “to preserve the blood of the Palestinian people”, expressing the government’s distinction between helping Hamas and helping Gazans.

Australian-Egyptian Middle East analyst Amro Ali says the distrust of Hamas’ perceived Muslim Brotherhood ties is highest in the security services, which blames both groups for insecurity in the Sinai Peninsula. The foreign ministry also bears responsibility for the crisis, as a “very conservative, regressive” faction has taken charge of policy relating to Hamas and Gaza, he says.

Hamas, however, has its own problems disrupting the relationship. American University of Cairo’s Dr Gamal Soltan says Hamas is deliberately trying to undermine Egypt’s efforts. “It’s about rejecting the Egypt initiative, not engaging with it at all, and insisting on bringing in other regional actors … to play that role.” Soltan says despite the Hamas leadership complaining last week they had not been consulted about Egypt’s ceasefire announcement, moderate Moussa Abu Marzouk had in fact been part of the talks. His rival Khaled Meshaal, head of the dominant faction in Gaza and and the armed wing, objected to the Gaza-based faction not also being involved. Moreover, the “massive” public support in Egypt for Hamas and Gaza Palestinians disappeared particularly after Morsi was deposed, Soltan says.

In 2008 the Egyptian mainstream media heralded popular support for the Gaza cause, backed by public activism and fundraisers. Today, those same media outlets are “hostile” to Hamas and highly critical, while three years of protests and problems have left Egyptians apathetic. Language teacher Ahmed Madboly is sympathetic to Gazans’ plight and Hamas’ right to defend itself, but he says the organisation has become “crazy”, and he stopped supporting its goals once civilians were getting hurt.

Egyptians are generally sceptical about Hamas. Many believe it was involved in the “prison break” on January 29, 2011, when 34 Muslim Brotherhood members, including Morsi, escaped. Hamas denied any involvement. Morsi is also one of 35 Islamists on trial for conspiring with foreign groups to commit acts of terrorism in Egypt, a charge that implicates Hamas and Lebanon’s Hezbollah.

Yet Ali says social justice was key in the 2011 revolution, and President Abdel Fattah el-Sisi’s honeymoon period is rapidly eroding. He believes Egyptians will soon begin questioning why their country is not doing more to help their traditional allies, the Gaza Palestinians.