In asking Francis to intervene, Fernandez said she recalled how Pope John Paul II averted war in 1978 between Argentina and Chile over three tiny islands in the Beagle Channel at the southern tip of South America.
With military governments on both sides poised for battle, he sent his personal envoy to mediate the crisis through shuttle diplomacy between Santiago and Buenos Aires, and eventually brought both governments to the Vatican to consider his compromise.
The conflict wasn't entirely resolved until after democracy returned to Argentina, and both sides signed a "treaty of peace and friendship" at the Vatican in 1984, giving the islands to Chile but maritime rights to Argentina.
On Monday, Fernandez gave Francis a picture of a marble monument honoring the 30th anniversary of John Paul II's negotiations, and then used the opportunity to bring up the issue of sovereignty over the Falklands.
They also seemed to have patched up their relationship.
Fernandez gave the new pope a mate gourd and straw, to hold the traditional Argentine tea that Francis loves, and he gave her a kiss.
"Never in my life has a pope kissed me!" Fernandez said afterward.
As the meeting was under way Monday, the Vatican released details of Francis' installation Mass, saying it would be a simplified version of the 2005 installation Mass that brought Pope Benedict XVI to the papacy, with only a half-dozen cardinals pledging their obedience to him and many gestures to Eastern rite Catholics and Orthodox Christians in a sign of church unity.
Francis is familiar with Orthodox traditions from 14 years of heading the Argentine church's commission on Eastern Rite Christians, who are within the Catholic fold but follow Orthodox religious customs, including some married clergy in lower ranks.
In all, some 33 Christian delegations will be present, as well as representatives of Jewish, Muslim, Buddhist, Sikh and Jain communities.
Those who knew Jorge Mario Bergoglio as leader of Argentina's Catholic Church say promoting interfaith dialogue was at the heart of his view of the what the Catholic faith should be about — an outward-reaching, bottom-up effort to improve lives, no matter what people's faith.
"He's the one who opened the cathedral of Buenos Aires for interfaith ceremonies, like when we prayed for peace. He's not one of those who waits for you to call them to participate in these events — he promotes them,"Buenos Aires Rabbi Alejandro Avruj told The Associated Press on Monday.
For Jews, Orthodox and other religious leaders, the new pope's choice of Francis as his name is also important for its reference to the Italian town of Assisi, where Pope John Paul II began conferences encouraging interfaith dialogue and closer bonds among Christians.
The Vatican also released details of Francis' coat of arms and official ring, both of which are in keeping with his style and priorities: The coat of arms is the same Jesuit-inspired one he used as archbishop of Buenos Aires, featuring symbols of Mary, Jesus and Joseph, albeit with the papal trappings of a bishop miter and the crossed keys of the Holy See. The ring was once offered to Pope Paul VI, who presided over the second half of the Second Vatican Council, the church meetings that modernized the church.
Francis will officially receive the ring and the pallium, a wool stole, during Tuesday's installation.
Michael Warren in Buenos Aires and Suzan Fraser in Ankara contributed.
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