Its political leaders in exile, Mr Meshaal included, have therefore had a transitory life.
The Palestinian Islamist group Hamas has re-elected Khaled Meshaal as its political leader, officials said.
Mr Meshaal himself had indicated last year that he would not be seeking a new term.
Meshaal was re-elected as chairman of the Hamas Political Bureau in Cairo on Monday.
"We are forging ahead with the reconciliation, " Mr Meshaal told the BBC's Hardtalk programme.
Jordan closed the bureau in the late 1990s and briefly jailed Mr Meshaal before expelling him to Qatar.
Khaled Meshaal became Hamas's political leader when its founder Sheikh Ahmed Yassin was assassinated by Israel in 2004.
Carter also asked Hamas to release Shalit, Meshaal said after the former president's visit, but the request was rejected.
Former President Jimmy Carter held a controversial meeting with the group's leader, Khaled Meshaal, in April of this year.
Mr Meshaal then headed to Syria, where he became political leader in exile.
Mr Meshaal also said preparations were being made for presidential and parliamentary elections.
Meshaal promised Carter then that Hamas would allow Shalit to send a message to his parents, Noam and Aviva.
Mr Meshaal has headed Hamas, the group that governs the Gaza Strip, since the assassination of its founder in 2004.
Earlier this month, Hamas celebrated its 25th anniversary in Gaza with a rally attended by exiled political leader Khaled Meshaal.
But, in an official statement, Hamas urged Mr Meshaal - who lives in exile in Syria - to reconsider his decision.
Correction: This report has been amended to remove a line saying that Khaled Meshaal said President Assad continued to support Hamas.
Mr Abbas and Hamas leader Khaled Meshaal signed a reconciliation deal in Cairo in 2011, but it has not been implemented.
BBC: Gaza: Fatah holds biggest rally since Hamas came to power
In a speech during a visit to Gaza last month, Mr Meshaal urged "reconciliation and national unity of the Palestinian ranks".
BBC: Gaza: Fatah holds biggest rally since Hamas came to power
Last week, Mr Mursi held talks with Hamas's political leader, Khaled Meshaal, and Palestinian Authority President Mahmoud Abbas, who heads Fatah.
BBC: Egypt's president discusses Gaza blockade with Hamas PM
Meshaal arrived in Tehran for his first visit to the country since Israel's recent military offensive on Gaza, Iranian media reported.
Meshaal -- who lives in exile in Syria -- is the head of Hamas, which rules the Palestinian territory of Gaza.
The agreement followed talks, the first in 18 months, between Palestinian leader Mahmoud Abbas of Fatah and exiled Hamas leader Khaled Meshaal.
But in February 2012, Mr Meshaal and the rest of the political leadership in exile moved from Syria to Egypt and Qatar.
The political leader of the Palestinian Islamist movement Hamas, Khaled Meshaal, does not want to stand for re-election this year, the movement says.
Hamas leader Khaled Meshaal has told the BBC he is in talks with Palestinian President Mahmoud Abbas about forming a national unity government.
Morsy said he invited Palestinian Authority President Mahmoud Abbas to meet with Khaled Meshaal, the political leader of Hamas, who lives in Cairo.
Our correspondent says Mr Meshaal's decision will please those in Gaza who see themselves as more hardline and committed to the struggle with Israel.
In 2011, Mr Meshaal and Palestinian Authority President Mahmoud Abbas - the Fatah leader - endorsed an Egyptian plan to reconcile the rival factions.
Mr Meshaal this year strongly supported Mr Abbas's move in upgrading Palestinian status at the United Nations to that of a non-member "observer state".
Born near Ramallah in the occupied West Bank, Mr Meshaal has spent decades in exile and visited Gaza for the first time in December.
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