I know Vic is banned and all, but I can't stand misinformation. The US Army decided they needed to upgrade, after they saw the difference in performance between the Krag-Jorgensen and the Mauser type rifle the Spanish were using in the Spanish-American War (1898). They did not base the M1903 on captured Mausers, rather they purchased the rights to the Mauser bolt action for 200,000$ after prolonged negotiations with the Mauser Company.
The action of the experimental rifle that eventually became the M1903 was based in part on captured Mauser M1893s. The design for the rifle was finalized in 1900, when many countries were just receiving their Model 1898s, and understandably these countries were not too eager to give them up for evaluation.
And though some 80,000 rifles were produced starting in 1903, it wasn't distributed as a front-line weapon until 1906.