Vatican spokesman Federico Lombardi appears to have tried to avert the gathered media from depicting the incident as a failure in international diplomacy, saying the pope was likely to have uttered "eso no sabía bien" (I didn't know that) in confusion at the origins of the present, and not "eso no está bien" ("this is not right"), as some outlets have reported.
Bolivian officials said the gift was a replica of a crucifix made by the late Father Luis Espinal, who was gunned down by a paramilitary death squad in 1980.
Mr Morales, who once referred to the Catholic faith as his "main enemy," had a tenuous relationship with the Church prior to Pope Francis's arrival.
Despite the awkward encounter in Bolivia, history's first Latin American pope "humbly" begged forgiveness during a meeting with indigenous groups and other activists and in the presence of Bolivia's first-ever indigenous president, Morales.
Francis noted that Latin American church leaders in the past had acknowledged that "grave sins were committed against the native peoples of America in the name of God".
St John Paul II, for his part, apologised to the continent's indigenous for the "pain and suffering" caused during the 500 years of the church's presence in the Americas during a 1992 visit to the Dominican Republic.
But Francis went farther, and said he was doing so with "regret".
"I would also say, and here I wish to be quite clear, as was St John Paul II: I humbly ask forgiveness, not only for the offences of the church herself, but also for crimes committed against the native peoples during the so-called conquest of America," he said to applause from the crowd.
Then deviating from his prepared script, he added: "I also want for us to remember the thousands and thousands of priests who strongly opposed the logic of the sword with the power of the cross. There was sin, and it was plentiful.
"But we never apologised, so I now ask for forgiveness. But where there was sin, and there was plenty of sin, there was also an abundant grace increased by the men who defended indigenous peoples."
Francis' apology was met with wild applause from the indigenous and other grass-roots groups gathered for a world summit of popular movements whose fight against injustice and social inequality has been championed by the pope.
The apology was significant given the controversy that has erupted in the United States over Francis' planned canonisation of the 18th century Spanish priest Junipero Serra, who set up missions across California.
Native Americans contend the priest brutally converted indigenous people to Christianity, wiping out villages in the process, and have opposed his canonisation. The Vatican insists he defended natives from colonial abuses.