Pope Francis today urged leaders of a Roman Catholic Church riven by scandal and crisis never to give in to discouragement and bitterness but to keep their eyes on their true mission.

"Let us never give in to the pessimism, to that bitterness, that the devil places before us every day. Let us not give into pessimism and discouragement," he told cardinals gathered in the Sistine Chapel to greet him.

Since his election on Wednesday night as the first non-European pope in nearly 1,300 years, Francis has been laying out a clear moral path for the 1.2-billion-member Church, which is beset by scandals, intrigue and strife.

His initial actions suggest he will bring a new style to the papacy, favouring humility and simplicity over pomp and grandeur.

In the Sistine Chapel, the same place where he was elected, he spoke to the cardinals in Italian from a prepared text but often added off-the-cuff comments in what has already become the hallmark of a style in sharp contrast to his predecessor, Pope Benedict.

He told the cardinals that the role of older people in the Church was to pass on optimism and hope to younger generations looking for spiritual guidance in a modern world full of temptations.

"We are in old age. Old age is the seat of wisdom," he said, speaking slowly. "Like good wine that becomes better with age, let us pass on to young people the wisdom of life."

During the meeting he briefly stumbled as he descended the steps in front of his throne to greet Angelo Sodano, dean of the cardinals, but he quickly recovered his balance.

After his address, Francis jovially greeted each of the some 150 cardinals in the room. He remained standing while spending about a minute with each of them and often broke into laughter.