Whether I need to separately register my marriage in the U.S. when pursuing a marriage-based green card

Hello. I’m an employed person preparing for a green card through marriage. My spouse and I already registered our marriage in Korea and had our wedding ceremony, but the marriage isn’t registered in the U.S.

In this case, I’d like to know if I need to separately register in the U.S. as well, and submit that for the green card process.