Methods are provided for producing compositions, e.g. pastes or clays, which rapidly set into high-strength calcium phosphate products. In the subject methods, dry reactants that include calcium and phosphate sources, as well as a monovalent cation dihydrogen phosphate salt, are combined with a setting fluid and the combined reactants are mixed to produce the settable composition. A feature of the invention is that cements rapidly set into high strength product compositions. Also provided are the compositions themselves as well as kits for preparing the same. The subject methods and compositions produced thereby find use in a variety of applications, including hard tissue repair applications.