The U.S. Mint's gold-coin sales slid for a third consecutive year in 2012, as high prices and competition from other gold investment products limited demand for the coins.

The U.S. Mint sold 753,000 troy ounces of American Eagle gold coins in 2012, according to data posted on its website, down 25% from a year earlier and the lowest full-year sales since 2007.

The...