The new Pope, elected on Thursday, called for an "authentic and lasting peace" in Ukraine and a ceasefire in Gaza and release of all Israeli hostages held by militant group Hamas.
Leo also welcomed the recent ceasefire between India and Pakistan, negotiated overnight, and said he was praying to God to grant the world the "miracle of peace".
"No more war!" the Pope said, repeating a frequent call of the late Pope Francis and noting the recent 80th anniversary of the end of World War II, in which some 60 million people were killed.
Leo said today's world was living through "the dramatic scenario of a Third World War being fought piecemeal", again repeating a phrase coined by Francis.
The new Pope said he carried in his heart the "suffering of the beloved people of Ukraine".
Hours after Russian President Vladimir Putin proposed direct talks with Ukraine aimed at ending the bloody three-year war, Leo appealed for negotiations to reach an "authentic, just and lasting peace".
The Pope also said he was "profoundly saddened" by the war in Gaza, calling for an immediate ceasefire, humanitarian aid and release of the remaining hostages held by Hamas.
Leo said he was glad to hear of the recent India-Pakistan ceasefire and hoped negotiations would lead to a lasting accord between the nuclear-armed neighbours.
He added: "But there are so many other conflicts in the world."
Leo, the former Cardinal Robert Prevost, is the first US-born pontiff and was a relative unknown on the world stage before his election on Thursday.
He previously served for decades as a missionary in Peru before first becoming a cardinal to take up a senior Vatican role two years ago.
Leo's first Sunday address to tens of thousands in the square coincided with a previously planned pilgrimage to Rome by marching bands from around the world.
Minutes before the Pope addressed the crowd, bands marched up the broad boulevard leading to the Vatican playing songs such as Y.M.C.A. by the Village People, the theme from the film Rocky, and music by John Philip Sousa, who composed the marching classic Stars and Stripes Forever.
The crowd, estimated at more than 100,000 by Italian authorities, was also entertained by bands from Italy, Mexico and other parts of Latin America who came to Rome for the ongoing Catholic Holy Year.
Leo gave his address on Sunday in fluent Italian.
In all of his appearances since his election, Leo has not made any mention of the country of his birth, angering some US conservative commentators.
Leo is a member of the Augustinian religious order, which runs the Shrine of Our Lady of Good Counsel in Genazzano.
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