"Egypt's recent serious effort aims to break the deadlock that has hung over peace efforts," he said in a speech broadcast live on state TV.
"It is a sincere effort to make everyone face their responsibilities and warn of the consequences of delays in achieving peace," he said.
His remarks followed a trip by Egypt's Foreign Minister Sameh Shoukry to Israel earlier this month, the first such visit in nine years.
Sisi said in May that Egypt was willing to take part in peace talks, saying there was a "real opportunity" for an Israeli-Palestinian deal that could lead to warmer ties between his country and Israel.
Israeli Prime Minister Benjamin Netanyahu, who met Shoukry during his visit, welcomed Sisi's offer.
Shoukry also met Palestinian leaders in the West Bank city of Ramallah.
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The last round of Israeli-Palestinian peace talks collapsed in April 2014.
In 1979, Egypt was the first Arab state to sign a peace treaty with Israel after years of conflict. It remains an influential player in the region.
However, ties between the countries have been cold over Israel's policies toward the Palestinians.
Netanyahu has called on Palestinians to engage in direct negotiations with Israel, but Palestinian leaders say years of talks have not ended Israel's occupation of the West Bank and Gaza.
Palestinian president Mahmud Abbas has instead tried to put pressure on Israel through diplomacy at the UN.
In June, representatives from 28 Arab and Western countries, the Arab League, European Union and the United Nations met in Paris to discuss ways push peace efforts forward.
Neither Israeli nor Palestinian representatives were invited to attend the meeting, which aimed to prepare for a peace conference by the end of the year.
The Palestinians have welcomed the French bid but Israel strongly opposes the initiative.