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.
Blessings were allowed last month in a document called Fiducia Supplicans (Supplicating Trust), which has caused widespread debate in the Catholic Church.
Netanyahu sent a letter to the Pope on Sunday after appealing to 33 female leaders worldwide, including First Lady Jill Biden, in previous weeks.
Defending Israel's right to self-defense, Chief Rabbi of South Africa Dr. Warren Goldstein accused the Pope of "primitive pacifism."