Hamas says it will resume fighting unless the border crossings into Gaza are reopened and Israel ends its 18-month economic blockade of the territory.
The group is trying to negotiate a deal that would allow the Rafah crossing into Egypt to stay open, even if monitors from the EU or security forces from the Palestinian Authority (PA), which is currently controlled by Fatah, are not present.
"We reject an open-ended ceasefire, but temporary calm with guarantees can be discussed," Fawzi Barhoum, a Hamas official, told the Associated Press news agency.
The fate of Gilad Shalit, an Israeli soldier captured by Palestinian fighters in June 2006, was also reported to be on the meeting's agenda.
Israel has demanded that arms trafficking into the Gaza Strip is halted and has called on Cairo to do more to stop smuggling through tunnels from Egypt.
"Israel considers that Egypt is in a position to confront the matter of arms smuggling and to put an end to it," Amos Gilad, a senior Israeli envoy, said on Saturday.
European Union diplomats were also set to discuss the border issues when they meet the foreign ministers of Egypt, Jordan, Turkey and the Palestinian Authority.
The EU is expected to offer monitors, ships and radar equipment to help secure Gaza's borders and halt smuggling. France has already sent a naval vessel to the region.
The talks come after rival leaders from Hamas and Fatah expressed hopes for more unity following Israel's war on Gaza.
Bloody fallout between the two main Palestinian groups in June 2007 resulted in Fatah being left to rule the West Bank and Hamas gaining control of the Gaza Strip.
"We have to sit together, to talk together, in order to face the Israeli plan in our land"
Ghazi Hamad, former spokesman for Ismail Haniya, Hamas leader in Gaza
The Rafah crossing, and six border points into Israel, have largely remained closed since.
Palestinians from both sides now say the rival groups need to set aside their differences.
"The Israelis, when they came, they were not discriminating between Fatah and Hamas - they were attacking everyone," Faisal Abu Shahla, the director of al-Shifa hospital in Gaza, told Al Jazeera.
Abu Shahla, a supporter of Fatah, urged reconciliation between the two parties, saying anything less would be to ignore the will of ordinary Palestinians.
"The people of Gaza sent a message to politicians: we want you to be unified, and to have unity. Any talk about the sake or benefit of Hamas or Fatah is [a] failure, and not representative of the people," he said.
Ghazi Hamad, the former spokesman for Hamas leader Ismail Haniya, joined the renewed calls for unity, saying it was "a disaster" that Fatah and Hamas remained divided.
"We have to sit together, to talk together, in order to face the Israeli plan in our land," he said.
"This is very important, because the main conflict is not between Fatah and Hamas, it is between Palestinians and Israel."
Al Jazeera's Nour Odeh, reporting from Ramallah in the West Bank, said: "They all realise that international money for reconstruction will not be earmarked to a specific Palestinian faction, it will be earmarked to the Palestinian Authority.
"That is really the point that Egypt is trying to push."