Last week, residents of the South Atlantic islands overwhelmingly voted to remain under British rule.
Fernandez said she and Francis also discussed human trafficking and slavery.
Vatican: Argentine claims defamatory
The Vatican has sought to quell controversy over Pope Francis' conduct during Argentina's so-called Dirty War from 1976 to 1983, amid accusations that he could have done more to protect two Jesuit priests who were kidnapped.
The accusations resurfaced after the Argentine cardinal's unexpected election to the papacy last week.
A book by investigative reporter Horacio Verbitsky accuses Francis, who was then Jorge Mario Bergoglio and was head of the country's Jesuit order, of deliberately failing to protect the two priests, Orlando Yorio and Francisco Jalics, when they were seized by the navy. They were found alive five months later.
But the Rev. Federico Lombardi, the Vatican's lead spokesman, dismissed the claims as false and defamatory.
"The campaign against Bergoglio is well-known and goes back to many years ago. It was promoted by a defamatory publication," he said at a Vatican news conference Friday.
"This was never a concrete or credible accusation in his regard. He was questioned by an Argentinian court as someone aware of the situation but never as a defendant. He has, in documented form, denied any accusations," Lombardi said.
"Instead, there have been many declarations demonstrating how much Bergoglio did to protect many persons at the time of the military dictatorship," he said.
His role after he became bishop of Buenos Aires in asking for forgiveness for the church for not having done enough at the time of the dictatorship "is also well-known," Lombardi said.
First Sunday as pope
Thousands of Catholics waving flags from around the world packed St. Peter's Square on Sunday to hear Pope Francis deliver his inaugural Angelus.
The new pontiff gave the noon blessing from the papal apartment window, speaking to more than 200,000 worshippers in the square four days after his election as pope.
"Dear brothers and sisters, good morning," he said in Italian, drawing cheers from the crowd.
During the 15-minute address, he focused on forgiveness.
"Never forget this: The Lord never tires of forgiving us," he said. "Have you thought about the patience that God has with each of us?"
He made the historic address after celebrating Mass at Sant'Anna parish in Vatican City earlier Sunday.
Reforms to come?
In his first week as pontiff, Francis has enjoyed global fanfare as the first Latin American pope and the first Jesuit pope in modern times. In just his first few days, he has prompted speculation that he may bring in wider changes.