Francis has repeatedly deplored the death and destruction in the Gaza war.
In previous years, Francis would start it prostrating himself on the marble floor of the basilica, but his physical condition no longer allows him to do so.
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"We should never forget that war is always a defeat," Pope Francis said.
"I have asked that studies be carried out into this ugly ideology of our times, which cancels out the differences and makes everything the same," the pope said.
Milei, a maverick right-wing libertarian, in the past called Francis an "imbecile," a "son-of-a-bitch preaching communism" and the devil's man on earth.
In his letter, the pope also called, once again, for the release of those hostages still being held by Hamas.