"In God's eyes, nothing is received in vain!" the Pope told Monaco's royal family and leading residents.
"Every good placed in our hands... bears an intrinsic need not to be held back, but to be shared, so that everyone's life may be better."
Leo is the first Pope in nearly five centuries to visit the wealthy Mediterranean enclave. He arrived after a 90-minute helicopter ride from the Vatican and met first with Prince Albert, Monaco's head of state and son of the late Hollywood star Grace Kelly.
The Pope appeared to reiterate his message that the wealthy should help those less fortunate in his official gift to Albert.
He gave the prince a colourful artwork created by the Vatican's mosaic studio, an image of St Francis of Assisi, a 13th-century son of a prosperous Italian merchant who renounced his inheritance to help the poor.
The second smallest state in the world after the Vatican, and one of the last countries with Catholicism as the state religion, Monaco has the highest concentration of billionaires per capita in the world.
In his speech at Albert's official residence, a 12th-century fortress with lavish apartments overlooking blue-green Mediterranean waters, Leo urged Monaco's residents to "put your prosperity at the service of law and justice".
Leo, the first US Pope, was elected in May to succeed the late Pope Francis as head of the 1.4-billion-member Church. His visit to Monaco is only his second outside Italy, but opens what is expected to be a busy year of travel.
Leo, 70, is relatively young and in good health for a Pope. He will undertake an ambitious, four-country tour of Africa in April, and is also due to make a week-long visit to Spain in June.
