An Israeli official said that during the meeting, Mr Netanyahu asked for Egypt's help in returning the bodies of two Israeli soldiers held by Hamas in Gaza, as well as two Israeli civilians detained by the Islamist movement in the Palestinian enclave.
His trip is seen as a sign of strengthened ties between two countries sharing deep concerns over regional unrest. In Sisi's impromptu and unusual foreign policy speech in May, he said "we will achieve a warmer peace if we resolve the issue of our Palestinian brothers", and he asked the Israeli leadership to broadcast his words throughout its country.
Palestinians are seeking the establishment of an independent Palestinian state in the West Bank and Gaza Strip, with East Jerusalem as the capital - territories occupied by Israel in the 1967 Arab-Israeli war.
Palestinian leaders say years of direct talks with Israel have not ended the almost 50-year occupation of Palestinian territories, and they have instead chosen to pursue worldwide diplomacy to reach a deal.
Netanyahu and other Israeli officials have expressed their appreciation of al-Sisi's statements and stressed the importance of involvement of Arab states in the region in attempts to end the Israeli-Palestinian conflict in recent months.
Netanyahu welcomed the Egyptian initiative.
The situation changed since al-Sisi took power, and a new Egyptian ambassador presented his credentials to the Israeli president in February.
And it warned of "perpetual occupation and conflict" between both sides.
Israeli soldiers check a auto as they block vehicles from crossing from the West Bank city of Hebron to Yatta village on July 6, 2016, as Palestinians try to enter the village to visit relatives to celebrate the Eid Al-Fitr holiday.
The two countries have increased coordination in the restive Sinai Peninsula, where Egypt is battling insurgents who have pledged allegiance to Islamic State.
At a press conference prior to retiring to the Prime Minister's office for their meeting, Netanyahu hailed the peace treaties between Israel and Egypt and between Israel and Jordan as a "cornerstone of stability for the region".
The summit provided some positive optics for Netanyahu, whose right-wing administration has faced growing criticism from Europe and the United States over the stalled peace negotiations and Israel's continued expansion of settlements in the West Bank. US Secretary of State John Kerry was the last American to falter in the 2013-14 Israeli-Palestinian peace talks.
Furthermore, the three dailies highlighted Israeli diplomatic to foil a vote on a Palestinian-Jordanian draft concerning Israeli violations against Al-Aqsa Mosque compound during the 40 annual session meeting of UNESCO's World Heritage Committee. He said Shoukry "answered in the affirmative".
Most of the Palestinians killed were carrying out knife, gun or car-ramming attacks, according to Israeli authorities.