"What's happened with this song is just insane," said Fonsi, who hails from Puerto Rico and sings in Spanish.
"I don't want to use the word accident because I was trying to write a hit, but I didn't plan for it to cross over.
"I just wanted to make people dance."
The 39-year-old said the global success of his song - which has reached number one in more than 45 countries, including the UK - gave him hope in the current political climate.
"I come from Puerto Rico and I live in Miami. We're living in an interesting time right now when people want to divide us. They want to build walls.
"And for a song to bring people and cultures together, that's what makes me proud."
Despacito is a sun-bleached slice of sensual reggaeton. The title translates as "slowly", referring to the speed of Fonsi's seduction technique.
It hit number one around Latin America when it was released in January, but only caught fire in the English-speaking world after Justin Bieber heard the song in a nightclub and asked to add a verse.
His version of the song - known as Despacito (Remix) - has become a phenomenon on streaming services, most notably Spotify and Apple Music. It is already the fourth most-played video of all time on YouTube, where it is rapidly closing in on the top three, all of which are years old.
The head of Universal Music Group, Sir Lucian Grainge, said the success of Despacito showed how streaming was democratising the music market.
"Streaming has allowed a song with a different beat, from a different culture, in a different language, to become this juggernaut of success and pleasure," he told the BBC.
"The industry has predominantly been English-speaking artists for the last 50 years [but] streaming will continue to open up music from Latin America artists globally.
"Anything and everywhere is up for grabs."
Of course, records will continue to be broken alongside the growth of streaming services - which give users access to a vast library of on-demand music for a monthly fee.
In March, Spotify announced it had attracted 50 million subscribers. Apple Music, which is yet to reach its second birthday, has already attracted 27 million paying customers; while Google Play, Amazon Unlimited, Deezer and YouTube and dozens of others have contributed to Despacito's success.
Critics might point out that the song would never have achieved such visibility without Bieber's contribution, but Sir Lucian was candid about how Universal had harnessed the star's brand power.
"Bringing in Justin Bieber meant that we could take something that was well on its way, and really take it to heights that would have been perceived as unimaginable when the song was written," he told the BBC.
"We were at one level, and he helped us get to the next."
Fonsi also paid tribute to Bieber's contribution, and reflected on his breathtaking success in a phone interview from Lisbon.
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