Sameh Shoukry's visit to Israel - the first by an Egyptian foreign minister in nine years - follows a similar meeting with Palestinian officials in Ramallah on June 29.
Solving the Israeli-Palestinian conflict will make the peace treaty between Egypt and Israel "warmer", Al-Sisi said in May, adding that Egypt is ready to mediate to end the conflict.
He also participated in the ministerial meeting in Paris in early June, which aimed to bring the Israelis and the Palestinians into negotiations based on a French initiative.
The peace process between Israel and Egypt has always been a "cold" one, and the latter years of the Hosni Mubarak regime saw few meaningful diplomatic interactions. The initiative offered full recognition of Israel but only if it gave up all land seized in the 1967 Middle East war and agreed to a "just solution" for Palestinian refugees.
He added that peace between Israelis and Palestinians "would have dramatic and positive results and on the situation in the entire Middle East", and warned of maintaining the status quo, which might ignite further escalation.
Shoukry affirmed the Egyptian stance to Abbas, supporting the restoration of peace talks between Palestinians and Israelis. "For Israel it's important because it shows the willingness to cooperate on a regional level on a regional solution to the Israeli Palestinian conflict".
"As happened in all previous instances, when deeds attributed to Prime Minister Netanyahu turned out to be baseless, here as well there will be nothing, because there is nothing", said Nir Hefetz, an adviser to the Netanyahu family.
A former senior Israel official said his country has conducted numerous drone attacks on militants in Sinai in recent years with Egypt's blessing.
Netanyahu has said that he is willing to discuss variations on this plan.
However, relations of the two countries soured in 2012, when Israel embarked on a military operation in the Gaza Strip enclave, ruled by the Hamas Islamist Group.
Israeli settlements in the occupied West Bank are considered illegal under worldwide law and major stumbling blocks to peace as they are built on land Palestinians view as part of their future state.
After years of domestic upheaval in Egypt following the 2011 "Arab Spring", Sisi is trying to reestablish the mediating role that former President Hosni Mubarak once played before he was forced to resign, analysts said.
Netanyahu and Sisi last met in 2014 after Sisi took power.
Netanyahu's government is considered to be the most right-wing in Israel's history, and key members of his cabinet are strong supporters of settlement building and opponents of a Palestinian state.
Also on Sunday, Israeli forces arrested at least 16 Palestinians in occupied East Jerusalem and the rest of the West Bank, local media reported.