To investigate the composition and evolution of circumstellar ice around low-mass YSOs, we observed ice absorption bands in the near infrared (NIR) towards eight YSOs ranging from class 0 to class II, among which seven are associated with edge-on disks. We performed slit-less spectroscopic observations using the grism mode of the Infrared Camera (IRC) on board AKARI, which enables us to obtain full NIR spectra from 2.5 $mu$m to 5 $mu$m. The spectra were fitted with polynomial baselines to derive the absorption spectra. The molecular absorption bands were then fitted with the laboratory database of ice absorption bands, considering the instrumental line profile and the spectral resolution of the grism dispersion element. Towards the class 0-I sources (L1527, IRC-L1041-2, and IRAS04302), absorption bands of H$_2$O, CO$_2$, CO, and XCN are clearly detected. Column density ratios of CO$_2$ ice and CO ice relative to H$_2$O ice are 21-28% and 13-46%, respectively. If XCN is OCN$^-$, its column density is as high as 2-6% relative to H$_2$O ice. The HDO ice feature at 4.1 $mu$m is tentatively detected towards the class 0-I sources and HV Tau. Non-detections of the CH-stretching mode features around 3.5 $mu$m provide upper limits to the CH$_3$OH abundance of 26% (L1527) and 42% (IRAS04302) relative to H$_2$O. We tentatively detect OCS ice absorption towards IRC-L1041-2. Towards class 0-I sources, the detected features should mostly originate in the cold envelope, while CO gas and OCN$^-$ could originate in the region close to the protostar, where there are warm temperatures and UV radiation. We detect H$_2$O ice band towards ASR41 and 2MASSJ1628137-243139, which are edge-on class II disks. We also detect H$_2$O ice and CO$_2$ ice towards HV Tau, HK Tau, and UY Aur, and tentatively detect CO gas features towards HK Tau and UY Aur.
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