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.
Leo also welcomed the recent ceasefire between India and Pakistan, 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, which killed some 60 million people.
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".
He appealed for negotiations to reach an "authentic, just and lasting peace".
He 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 the militant group 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."
It comes after the Pope took his first trip outside the Vatican, heading about an hour's drive east of Rome for a visit to a Catholic shrine and stopping on the way back to pay respects at the tomb of his predecessor Francis.
Leo waved from the passenger side of a Volkswagen vehicle as he arrived at Rome's St Mary Major Basilica.
Entering the church to a few shouts of "Viva il papa" (Long live the Pope), Leo walked slowly to Francis' tomb, laying a white flower on it.
He then knelt in prayer for a few moments.
Leo made the trip to St Mary Major after travelling to the small town of Genazzano, where he had earlier visited a shrine dedicated to the Virgin Mary.
Leo, the former US cardinal Robert Prevost, was elected pontiff on Thursday (Friday AEST).
He is a member of the Augustinian religious order, which runs the Shrine of Our Lady of Good Counsel in Genazzano.
Leo shook hands and offered blessings to a few people in the crowd before entering the shrine.
At the end of the visit there, the Pope told those in the shrine that he wanted to come to pray for guidance in the first days of his papacy, according to a Vatican statement.
The late Pope Francis, who died on April 21, made surprise visits to Catholic sites near Rome quite frequently.
He asked to be buried at St Mary Major in a simple tomb, decorated only with an inscription of the word "Franciscus" - his name in Latin.
Francis had a special devotion to the basilica, another Marian shrine.
In the first days after his burial, more than 30,000 people packed the church to visit his final resting place.
Pope Leo signalled earlier on Saturday he would continue with the vision and reforms of Pope Francis, telling cardinals the late pontiff left a "precious legacy" that must be carried on.
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