Francis offered his "cordial good wishes" and hoped Trump would be granted "wisdom and strength in the exercise" of his office.
But the pontiff struck a cautionary chord in his message to Trump, imploring the former reality TV star to continue to help those who suffer the most.
"At a time when our human family is beset by grave humanitarian crises demanding farsighted and united political responses, I pray that your decisions will be guided by the rich spiritual and ethical values that have shaped the history of the American people and your nation's commitment to the advancement of human dignity and freedom worldwide," wrote Francis.
Earlier in Washington, Trump had placed his left hand on a bible used by Abraham Lincoln and recited the US presidential oath.
But in his inauguration speech, Trump gave little indication his thoughts matched the Pope's as he vowed to put "only America first" and make the country "rich again".
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