Israeli Prime Minister Naftali Bennett is holding talks with Egyptian President Abdul Fattah al-Sisi in the Red Sea resort of Sharm el-Sheikh.
It is the first official visit to Egypt by an Israeli prime minister in more than a decade.
According to the Egyptian presidency, the two leaders will discuss bilateral and regional issues, as well as ways to restart the Israeli-Palestinian peace process.
Mr Bennett, who took over as Prime Minister in June, accepted an invitation to visit Egypt last month.
Mr Netanyahu was the last Israeli head of government to make an official visit to Egypt in 2011, when he met then-President Hosni Mubarak just over a month before he was ousted by a popular uprising.
He was also reported to have travelled secretly to Egypt in 2018 for unofficial talks with Mr Sisi, who led the military’s overthrow of Mubarak’s democratically elected successor in 2013 in the aftermath of mass protests. They also met several times on the sidelines of the United Nations General Assembly in New York.
Egypt was the first Arab country to sign a peace treaty with Israel in 1979, but relations between the neighbours have been strained at times.
The details of Mr Bennett’s trip to the Sinai Peninsula on Monday were shrouded in secrecy for security reasons, and his meeting with Mr Sisi was only announced shortly before it started.
According to the Egyptian presidency, the two leaders were expected to discuss “a number of bilateral issues in various fields”, as well as regional and international developments and “ways and efforts to revive the peace process” between Israel and the Palestinians.
According to the BBC’s Yolande Knell in Jerusalem, serious progress on peace talks appears unlikely given that they broke down in 2014, and Mr Bennett, a nationalist politician, opposes the establishment of a Palestinian state.
However, our correspondent adds that there is hope that agreements on Gaza reconstruction can be reached.
After 11 days of fierce fighting between Israel and Palestinian militant groups in the territory, Egypt helped broker a ceasefire in May. At least 260 people were killed in Gaza, with 13 killed in Israel.
A surge in cross-border violence has put the ceasefire to the test in recent weeks.
After rockets were fired at Israel for the third night in a row, the Israeli military said earlier on Monday that it had struck targets belonging to the militant group Hamas, which controls Gaza.