The government says Phil Hogan chose the "correct course of action" by resigning.
The European Trade Commissioner says it was his decision to step down, saying the GolfGate row had become a "distraction" from his work and would only undermine it in the months ahead.
Commission President Ursula von der Leyen said she respected his decision and wished him well.
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Kerry Fine Gael MEP Seán Kelly says Phil Hogan had no other option.