The Ghanaian leader is in Egypt for an official visit that will also see him watch the Black Stars opening game of the 2019 Africa Cup of Nations.
President Akufo-Addo said his meeting with president el-Sisi was aimed at strengthening ties between their two nations.
The visiting president is expected in Ismailia to watch the Black Stars game against Benin later today, as they seek to start their AFCON campaign on a positive note.
President Akufo-Addo promised the Ghanaian squad earlier this month that he will be in Egypt to watch them play their AFCON opener.
Despite being one of Africa’s top football teams, the Black Stars have not won the AFCON title since 1982.
Fans across the West African country hope the current squad can change that this year.
The 2019 tournament began on 21 June, and is set to run until 19 July.
This is the first AFCON tournament played in the June-July window, falling in line with the international football calendar.
It is also the first tournament to have 24 participating teams. Previous editions had just 16 participants.