Speaking at a cryptocurrency conference in New York, Dorsey, who is also the chief executive of Twitter Inc, reiterated his support for the virtual coin, but noted that not everyone within Square shared his views, including members of the board.
"We have a lot of healthy skepticism in the company and a lot of people were certainly skeptics of this technology," Dorsey said. "There is still a lot of skepticism, and still a lot of debate and disagreements and fights, but that is where the magic happens."
He added that the "healthy discussion" around bitcoin extended "all the way at the board level", without elaborating on specifics.
In January, Square, a San Francisco-based company largely known for its credit card processing hardware for small businesses, began allowing users of its consumer payment service Cash App to buy and sell bitcoin.
The company made $34.1 million in revenue from the new bitcoin offering in the first quarter of this year, but its bitcoin costs were $33.9 million, according to a May shareholder letter.
Proponents of bitcoin say that it can help democratize finance by offering a way to bypass banks and governments, and conduct transactions more cheaply.
But it has failed to take hold as a payment for mainstream goods and services, in part because of extreme volatility, slow transaction processing, and widespread doubts about its long-term viability.
The volatility of bitcoin and other digital currencies have, however, made them attractive speculative assets. The price of one bitcoin peaked in December to almost $20,000 and has since dropped to less than half that.
Dorsey, a known bitcoin enthusiast, said he believes the internet will have its own "native currency." He said he hoped that would be bitcoin. "I am a huge fan," he said.
A spokesman for Square told Reuters that the company does not have figures to share on Dorsey's bitcoin and cryptocurrency holdings.
Dorsey said wider acceptance of bitcoin could help Square expand globally.
"If we were able to use it as a currency today (...) we could release our apps in every app store around the world," he said.
(Reporting by Anna Irrera, Editing by Rosalba O'Brien)
By Anna Irrera and Gertrude Chavez-Dreyfuss
