Final answer:
The strong nuclear force is responsible for holding protons together in an atomic nucleus, overcoming the repulsive electromagnetic force due to their like charges.
Step-by-step explanation:
The fundamental force that holds protons together within an atomic nucleus, despite their positive charge, is the strong nuclear force. This force is one of the four fundamental forces of nature, significantly stronger than the electromagnetic force at very short distances such as those found within an atomic nucleus. The strong nuclear force effectively overcomes the electrostatic repulsion between protons, which would otherwise repel each other due to having the same positive charge. At distances smaller than 10-15 meters, the nuclear force keeps both protons and neutrons bound together, forming stable atomic nuclei.