"When love fails, and it fails many times, we have to feel the pain of that failure, accompany the people who have felt the failure of their love," the pope said during the daily mass he holds in the Vatican.
"Don't condemn them! Walk with them!" he said, adding: "We have to be so close to the brothers and sisters who have suffered the failure of love in their lives".
Changing that doctrine could in turn alter Church rules on marriage annulments and raise broader questions about the institution of marriage, prompting lively exchanges between traditionalists and reformers.
Cardinal Philippe Barbarin, the archbishop of Lyon in France, told Vatican radio that a meeting of cardinals from around the world in the Vatican this month devoted "80 to 90 percent" of the time to discussing the issue.
Honduran Cardinal Oscar Andres Rodriguez Maradiaga, a member of the council of eight cardinals established by the pope to advise him, has taken a more lenient line and has asked Mueller to be "more flexible".
A survey by the Spanish-language network Univision in 12 mainly Catholic countries found that 75 percent of Europeans, 67 percent of Latin Americans and 59 percent of Americans were at odds with the Church on the issue, while in Africa 19 percent of respondents disagreed.
The German diocese of Freiburg im Breisgau last year said it was authorising re-married divorcees to receive Holy Communion on a case by case basis -- prompting a quick rebuke from the Vatican.
The issue would affect millions of Catholics around the world, with around a quarter of Catholic marriages ending in divorce in the United States alone.
Some theologians and clergymen have called for changes to facilitate the annulment of marriages in cases in which it could be argued that the wedding took place under social pressure or was not fully understood.
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