Generally speaking, a marriage performed outside the US that is valid in that jurisdiction is recognized in the US.
It’s important to ensure that you obtain a valid marriage license from local authorities if you choose to have a religious ceremony in the US or in another jurisdiction, because it’s the license that makes a marriage legal, not just the ceremony.
One giant caveat to US recognition of international marriages is in the area of same-sex marriages, which are legal in many countries around the world, while the US has a confusing patchwork of state and federal laws.
Because this area of family law is evolving so fast, and is so subject to politics, your best bet when you have questions about international marriage – whether same-sex or opposite-sex – is to consult the lawyers at Zelenitz, Shapiro & D’Agostino at 718-523-1111.