SYDNEY—The popularity in the U.S. of a silver coin emblazoned with a kangaroo has caught the Perth Mint by surprise, prompting one of the world’s largest mints to accelerate an expansion to meet demand among American investors and collectors.

Sales of silver coins from the Australian mint have doubled over the past year, far outpacing growth in demand for other coins including those made of gold and the U.S. Mint’s popular silver American Eagles.

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