If you are on GAP CAP you could. Otherwise, you need to have an H1B visa.
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I agree with Attirney Segal. You could travel to the U.S. using your F-1 only if you are on gap cap. Otherwise, you must obtain an H-1B visa to re-enter.
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If you already have any approved H-1B petition and your OPT was extended, its possible.
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Talk to your H-1B petitioning company's counsel and seek his advise.
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