Pope Francis warned on Thursday that the troubled Catholic Church risked becoming little more than a charity with no spiritual foundations if it failed to undergo renewal.
The 76-year-old Argentinian told the cardinals who elected him as Latin America's first pope that the Church could "end up a compassionate NGO".
"I would like all of us after these days of grace to have the courage to walk in the presence of the Lord," Francis said in his first mass, amid the splendour of the Sistine Chapel.
He warned the cardinals against "the worldliness of the Devil".
"Walking, building and confessing are not so easy. Sometimes there are tremors," the pope said, in a homily that will be scrutinised for clues to the style of his leadership.
The new head of the world's 1.2 billion Catholics, who was formerly known as Cardinal Jorge Mario Bergoglio, had begun his reign by meeting people in Rome and laying a bouquet of flowers in homage to the Virgin Mary in a basilica.
The pope also prayed at the altar of St Ignatius of Loyola, the founder of the Jesuit order to which he belongs.
He returned to the priests' quarters where he stayed before the conclave and settled his own bill.
The election of the son of an Italian emigrant railway worker, who was considered a rank outsider, was met with widespread surprise and expressions of hope for change in a Church riven by scandal and internal conflict.
His elevation was also seen as recognition of the Church's power in Latin America, which now accounts for 40 percent of the world's Catholics, while it is in decline in Europe.
"The choice of Bergoglio shows that the Church is determined not to remain in mourning for the crisis in Europe but has opened its doors to the revitalising energy of Catholicism's biggest continent," Vatican expert Luigi Accatoli told AFP.
Projecting an image as a simple man of the people, the pope chose to name himself after St Francis of Assisi, the 13th century saint who shunned the riches of his family to devote himself to God and the poor.
The Vatican revealed that, for the ride back to the conclave lodgings after Wednesday's election, Francis shunned the papal limousine with the "Vatican City State One" number plates and instead boarded a minibus with the cardinals.
It was in keeping with his image as a man who as archbishop of Buenos Aires chose to live in a modest apartment rather than the official residence and took buses to work.
-- Poisonous rivalries --
Experts said they expected the new pope to shake up the Vatican, where poisonous rivalries within the Curia -- its governing body -- plagued the papacy of Francis's predecessor Benedict XVI.
Benedict, 85, abruptly ended his eight-year papacy last month saying he lacked the strength to deal with the rigours of the job.
The Vatican confirmed that Francis had part of a lung removed as a boy, but its spokesman Federico Lombardi insisted: "This is not a handicap in his life.
"Those who know him have always seen him in good health."
Francis and Benedict are to meet within days.
The new pope is also the first non-European pontiff in nearly 1,300 years and the first from the Society of Jesus order, or the Jesuits, known for their work in education and promotion of social justice.
World leaders greeted his election, while the Organisation for the Islamic Conference said Muslim nations hoped "the relationship between Islam and Christianity will regain its cordiality and sincere friendship" during his papacy.
The pointed message reflected a rocky relationship between the two faiths that reached a low in 2006, when Benedict sparked fury across the Muslim world with remarks seen as linking Islam with violence.
Bergoglio is not without controversy.
He was only 36 when he was named to lead Argentina's Jesuits, a job he held for six years under the country's 1976-83 military dictatorship.
The future pope and other Catholic clergy were lambasted by leftist critics for failing to act against the "Dirty War" during which 30,000 people died or disappeared.
More recently, his opposition to gay marriage and contraception has brought him into conflict with the Argentine government of President Cristina Kirchner.
The Argentinian of Italian descent, the 266th pope, faces the immediate challenges of stamping his authority on the Vatican machinery and trying to coax back worshippers that are deserting churches across the West
The sexual abuse of children by paedophile priests stretching back decades cast a dark shadow over the conclave, which included several cardinals implicated in the scandals.
A US man who has just won a $1 million settlement for abuse at the hands of a Californian priest called for Francis to excise the "cancer" in the Church and defrock one of those cardinals, former Los Angeles archbishop Roger Mahony, for allegedly hushing up the abuse.
"I hope that our new pope defrocks ... Cardinal Mahony for his role in covering up the abuse that I suffered," Michael Duran said, while acknowledging: "I don't have high hopes for that."
Francis's inauguration mass will take place on Tuesday -- a significant date in the Catholic calendar because it is the Feast of St Joseph.