Qatar said it plans to leave OPEC after nearly six decades, a move seen as seeking to curry favor with the Trump administration and spurning neighboring Saudi Arabia.

The decision by the Persian Gulf emirate—which is locked in an 18-month diplomatic standoff with Saudi Arabia, the cartel’s kingpin—comes as OPEC faces strong headwinds. The cartel is struggling to craft an effective response to falling prices and under pressure from Washington to keep them low.

The...