Writing in The New York Times, Francis chastised governments that ignored "mounting deaths" and warned about other "unseen viruses" such as climate change.
The pontiff spoke favorably about protests for racial justice, while criticizing "populist leaders" and those who rail against coronavirus restrictions.
The photo featured Brazilian model Natalia Garibotto wearing lingerie.
The president-elect reiterated his pledge of 125,000 slots for refugees seeking to resettle in the U.S., striking a very different tone from Trump.
Biden, who will be America's second Catholic president, is a "Pope Francis Catholic" who chooses to emphasize common-good issues, one ally said.
High-ranking Catholic clergy dismissed reports that former Cardinal Theodore McCarrick was abusing seminarians and children, a Vatican investigation found.
Before becoming pope, Francis supported extending legal protections to gay couples in Argentina. Those comments are now putting the Vatican in a bind.
Biden was quoting the pope and stressing unity in America, but the Trump campaign made it look as if he was confused while speaking at a Georgia rally.
Francis apologized for not greeting well-wishers at his weekly general audience, pointing a finger at "this lady called COVID, who does us so much harm."
The pope has courted some criticism for declining to wear a mask when indoors, even though Vatican regulations call for masks indoors and out when social distancing cannot be guaranteed.