Prior to the U.S. Civil War, the United States was best defined as a regional power. Other countries saw the United States as the most important country in the Western Hemisphere. This was due mainly to its continued growth both economically and in terms of territory in addition to the Monroe Doctrine of 1823 that decreed that the United States would oppose any further European intervention in the New World.

However, after the Civil War and the Second Industrial Revolution, the United States grew to be one of the largest countries in the world economically. By 1890, it had eclipsed the United Kingdom as the world's largest national economy (this distinction ignored colonial claims) and it spanned from coast to coast. American intervention in the Boxer Rebellion in China at the end of the nineteenth century along with the U.K., France, Germany, Russia, Japan, Italy, and Austria-Hungary all but confirmed its world power status.

So to answer your question, the United States was definitely a world power at the time period you asked. It had the world's largest national economy as well as the legendary Great White Fleet and an increasing number of territorial gains that created that oft-labeled American Empire. Other nations did acknowledge that status whether it was through American growth overseas, American intervention abroad, or even simply through international trade and diplomacy (for example, Teddy Roosevelt brokered the deal that led to peace between Japan and Russia following the Russo-Japanese War in 1905).