Israeli Foreign Minister Gabi Ashkenazi tweeted ahead of his meeting with Egyptian counterpart Sameh Shoukry that it was "the first formal visit of an Israeli FM [foreign minister] in 13 years" to Egypt.
What did Ashkenazi and Shoukry discuss?
Shoukry stressed the need to refrain from all practices that lead to escalation, especially in the Palestinian territories, the Egyptian foreign ministry said in a statement following the talks.
Cairo called on Israel to consider the particular sensitivity associated with east Jerusalem, Al-Aqsa Mosque and all Islamic and Christian holy sites, the statement added.
Shoukry also reiterated Egypt's position on a two-state solution as "the only way to achieve a just and lasting peace."
Ahead of Sunday's talks, Ashkenazi said: "We will discuss establishing a permanent cease-fire with Hamas, a mechanism for providing humanitarian aid and the reconstruction of Gaza with a pivotal role played by the international community."
He also noted that his government was "fully committed" to repatriating Israeli prisoners held by Hamas.
A prisoner swap could be on the horizon, after Hamas spokesman Abdelatif al-Qanou, said Hamas is also open to discussing a prisoner swap with Israel.
Hamas leader Ismail Haniyeh is expected to visit Cairo later this week.
Hanan Ashrawi on Conflict Zone
Parallel talks in Israel
Also on Sunday, Egyptian President Abdel Fattah el-Sissi sent the country's intelligence chief, Abbas Kamel, to Israel for talks with Prime Minister Benjamin Netanyahu and other Israeli officials.
Netanyahu said the meeting in Jerusalem dealt with regional security issues and ways to prevent Hamas from siphoning off civilian aid to strengthen its capabilities.
Ahead of the talks, an Egyptian official told the Associated Press that the discussions would also touch on measures that would allow materials, electricity and fuel into the territory, as well as the possible expansion of maritime space allowed for Gaza fishermen.
The role of the Fatah-led Palestinian Authority, a rival Palestinian body to Hamas, is central in the talks and reconstruction process, the official reportedly said.
What triggered the latest round of fighting?
Tensions began earlier this month when several Palestinian families living in the east Jerusalem neighborhood of Sheikh Jarrah were threatened with eviction from their homes. Jewish settlers claim the properties were owned by Jews prior to 1948.
Israel postponed the court hearing on the case in order to defuse tensions.