These views are all part of what is now known as the "Monroe Doctrine." The Monroe Doctrine was a policy that opposed European colonialism in the Americas. The doctrine stated that any efforts on the part of European powers to take control of an independent nation in the Americas would be seen as a direct attack on America.
These comments sound threatening to Europe. However, Monroe also stated the need for "friendly" and "peaceful" relations between the two areas of the world. These statements are not contradictory. In fact, they are complimentary.
Monroe believed that Europe and the Americas were two different spheres of influence. Although they had been related for very long, they now represented different areas of the world with different independent nations. He did not want Europe to forget this fact. Nevertheless, he did not oppose imperialism or intervention per se. He opposed it when it represented a threat to America. Monroe hoped that the United States could influence nearby countries with no input from Europe. However, he hoped that this would not bring problems or hostilities between the two regions of the world.