Filing married status

My wife and I are both residents of a foreign country and have been living in the USA for over five years on non-immigrant visas. We are not green card holders or US citizens. We were married in our home country and our marriage is legally recognized there. I am currently employed in the USA, and my wife is finishing her master's degree here. Do we need to register our marriage in the USA, or is our foreign marriage recognized for tax purposes? Can we file our taxes as 'Married Filing Jointly' even though our marriage was registered outside the USA?

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