We report growth of epitaxial AlN thin films on c-plane sapphire substrates by plasma-assisted molecular beam epitaxy. To achieve two-dimensional growth the substrates were nitrided by nitrogen plasma prior to the AlN growth, which resulted in the formation of a two-dimensional single crystalline AlN layer. The formation of the two-dimensional AlN layer by the nitridation process was confirmed by the observation of streaky reflection high energy electron diffraction (RHEED) patterns. The growth of AlN thin films was performed on the nitrided AlN layer by changing the Al beam flux with the fixed nitrogen flux at 860$^{circ}C$. The growth mode of AlN films was also affected by the beam flux. By increasing the Al beam flux, two-dimensional growth of AlN films was favored, and a very flat surface with a root mean square roughness of 0.196 nm (for the 2 ${mu}m$ ${ imes}$ 2 ${mu}m$ area) was obtained. Interestingly, additional diffraction lines were observed for the two-dimensionally grown AlN films, which were probably caused by the Al adlayer, which was similar to a report of Ga adlayer in the two-dimensional growth of GaN. Al droplets were observed in the sample grown with a higher Al beam flux after cooling to room temperature, which resulted from the excessive Al flux.