Abstract We report on the results of systematic infrared 2.5-5$\mu$m spectroscopy of 45 nearby ultraluminous infrared galaxies (ULIRGs) at $z \lt$ 0.3 using AKARI IRC. This paper investigates whether the luminosities of these ULIRGs are dominated by starburst activity, or alternatively, whether optically elusive buried active galactic nuclei (AGNs) are energetically important, based on the strengths of 3.3$\mu$m polycyclic aromatic hydrocarbon (PAH) emission and dust absorption features at 3-4$\mu$m. Because of the AKARI IRC's spectroscopic capability in the full 2.5-5$\mu$m wavelength range, we can apply this energy diagnostic method to ULIRGs at $z\gt$ 0.15. We estimate the intrinsic luminosities of extended (several kpc), modestly obscured ($A_{V} \lt$ 15mag) starburst activity based on the observed 3.3$\mu$m PAH emission luminosities measured in AKARI IRC slitless spectra, and confirm that such starbursts are energetically unimportant in nearby ULIRGs. In roughly half of the observed ULIRGs classified optically as non-Seyferts, we find signatures of luminous buried AGNs. The fraction of ULIRGs with detectable buried AGN signatures increases with increasing infrared luminosity. Our overall results support the scenario that luminous buried AGNs are important in many ULIRGs at $z \lt$ 0.3 classified optically as non-Seyferts, and that the optical undetectability of such buried AGNs occurs merely because of a large amount of nuclear dust, which can make the sightline of even the lowest dust column density opaque to the ionizing radiation of the AGNs.