MOSCOW—An international firestorm erupted over the possibility that a Russian official could become the new president of global police agency Interpol, as Moscow denounced a demand by U.S. senators that the Trump administration block the candidacy of a Kremlin-backed nominee.

Interpol confirmed Tuesday that Maj. Gen. Alexander Prokopchuk a veteran Russian Interior Ministry official, had been nominated for president, amid allegations that Moscow has used the international police agency to go after political foes.

A...