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Leo was celebrating a Mass for Pentecost, one of the Church's most important holidays.
The new pontiff, who spent many years as a missionary in Peru, also warned against 'closing ourselves off in our small groups'.
As part of the ceremony, Leo will also formally receive two items as he takes up the papacy: a liturgical vestment known as a pallium, a strip of lambswool which represents his role as a shepherd, and a special band known as the fisherman's ring.
"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 the Second World War, which killed some 60 million people.
The newly elected pope first visited Kochi in 2004, when he was the superior general of the Order of Saint Augustine (OSA).
Pope Leo, who was born in Chicago but spent two decades as a missionary in Peru, said a few words in English before continuing his homily in fluent Italian.
The election came on the first full day of voting by the 133 cardinal electors, who secluded themselves behind the Vatican's medieval walls on Wednesday afternoon.
They burn the ballot papers and mix them with chemicals to show how proceedings are going -- black signalling no pope and white announcing a new pontiff.
During the conclave, cardinals are sequestered from the world and sworn to secrecy, their phones and computers confiscated, while they are shuttled between the Sistine Chapel for voting and two Vatican guesthouses to sleep and dine.
No pope has been elected on the first day of a conclave for centuries
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