The Egyptian leader addressed the summit, saying he would focus on security on the African continent.
"Our work must continue to improve peace and security in Africa in a holistic and sustainable manner," Sissi said. "Mediation and preventive diplomacy will remain one of the priorities of the African Union."
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The new African Union chairman said that "counter-terrorism requires the identification of those who support and finance it and combating them collectively. While we are aware of the difficulty and complexity of the struggle, this remains the only appropriate way to uproot terrorism and eradicate it."
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The rights group Amnesty International warned that Sissi's chairmanship might undermine the African Union's human rights mechanisms.
"During his time in power President Abdel-Fattah al-Sissi has demonstrated a shocking contempt for human rights. Under his leadership the country has undergone a catastrophic decline in rights and freedoms," said Najia Bounaim, Amnesty's North Africa Campaigns Director. "There are real fears about the potential impact his chairmanship could have on the independence of regional human rights mechanisms and their future engagement with civil society."
The rights group said Egypt since 2015 has orchestrated a sustained political attack against the African Commission on Human and Peoples' Rights, the body that aims to monitor African states' human rights records. "Dozens of cases alleging serious human rights violations have been lodged against Egypt at the ACHPR," it said.
Egyptian leaders have been absent from African Union meetings since 1995 when an assassination attempt was made on the life of former leader Hosni Mubarak.
Sissi's election brought to an end the one-year chairmanship of Rwanda's President Paul Kagame.
African Union chairmen set agendas of issues to be addressed during their one-year tenure.
During his tenure, Kagame dramatically challenged the election results in the Democratic Republic of Congo.