In this study, the effect of binary and ternary cementitious systems composed of portland cement, high-lime fly ash and silica fume on the compressive strength, alkali-silica reaction (ASTM C 1567) and drying shrinkage of mortar mixtures was researched. For this purpose, binary and ternary binders were prepared with partial replacement of cement with either fly ash (15wt% and 30wt%) or silica fume (5wt%) or both mineral admixtures (15wt+%5wt% and 30wt%+5wt%). An alkali reactive basalt aggregate was used in this study. It was found that partial replacement of cement with high-lime fly ash reduced the strength of mortar mixtures even up to 28-days. Besides, addition of 5% silica fume had not a significant effect on the early strength of fly ash-bearing mixtures. However, silica fume inclusion improved the 28-day strength of mixtures. In terms of alkali-silica reaction (ASR), the fly ash with lower lime content reduced the 14-day expansion more than that of fly ash with higher lime content. The opposite results were the case in 28-day ASR expansions. The ASR expansions of the fly ash-bearing mixtures were significantly reduced by the introduction of the additional 5% silica fume to these mixtures. However, silica fume incorporation remarkably increased the drying shrinkage values of the mixtures. Finally, fly ash with higher lime content was found to be more satisfactory in terms of compressive strength, alkali-silica reaction and drying shrinkage in the ternary binder system.