The Islamist Morsi affirmed his support for the Palestinians in the Gaza Strip which is ruled by Hamas, Meshaal said after the meeting.
"Morsi affirmed Egypt`s support for Palestinians in Gaza, which confirms a new era in relations between Egypt and the Palestinian cause," said Meshaal, in comments published by the Egyptian state news agency MENA.
Hamas hailed the "historic" meeting, the first between a delegation from the Palestinian movement and an Egyptian head of state.
Hamas leader Ismail Haniya will meet Morsi, for the first time, in Cairo next week, Haniya`s office said.
Israel and Egypt have partly blockaded Gaza, which neighbours both nations, since 2007, when Hamas violently routed Abbas`s Fatah from the coastal enclave.
Egypt`s ousted dictator Hosni Mubarak eased the blockade in 2010, but did not allow commercial traffic through the Rafah border crossing as Hamas had hoped.
Morsi, in the past an outspoken backer of the Palestinians who pledged during his campaign for the presidency to support their "right of resistance" against Israel, has adopted a more subdued tone since his election.
Under Mubarak, Egypt had tried to broker a reconciliation between Hamas and Fatah, which foundered amid accusations between the rivals.
Meshaal said Morsi would soon schedule a meeting with him and Abbas to push the unity deal.
Fatah, which governs the West Bank, and Hamas, which controls the Gaza Strip, signed a national reconciliation agreement in April 2011 in Cairo under Egyptian mediation.
Under this deal the two governments should make way for a non-partisan transitional executive charged with organising elections within a year. However the text remains a dead letter. (AK)
Editor: Kunto Wibisono
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