This song used to play on the local hits station sometime between 1990 and 1996, maybe a little bit later, so I think it was a mainstream song in the United States at the time.

It was gently upbeat, with large instrumental synth sections, one in particular was very airy with a ney flute flourish that would make me imagine myself soaring between the reeds in the banks of the Nile river. There was a male vocal chorus that would repeat itself. I don't know if the lyrics were true gibberish or if I simply could not understand them, but the start of the chorus sounded something like
"oom dai, oom dio" before going on to more complicated lyrics.

Thank you so much for your help! Have a great weekend!

I know music and this is not enough to ID the song - in my opinion.

Maybe It was a more oriental feel? Well, I knew it was a long shot. Thanks for trying ^_^

Hey, I found it! Thanks again!

Have you looked at any of Enigma's songs or videos?

You nailed it! After spending a day checking 1990's Billboard lists, I've discovered that my mystery song was really my fuzzy childhood memories fusing the chorus from "I Want You" by Savage Garden ("Oom dai, Oom dio" is actually "Ooh, I want you, I-") into Enigma's "Sadeness". Thanks for the advice!