Large language models (LLMs) have received a lot of attention in natural language processing (NLP) research because of their exceptional performance in understanding and generating human languages. However, low-resource languages are left behind due to the unavailability of resources. In this work, we focus on enhancing the LLaMA-2-Amharic model by integrating task-specific and generative datasets to improve language model performance for Amharic. We compile an Amharic instruction fine-tuning dataset and fine-tuned LLaMA-2-Amharic model. The fine-tuned model shows promising results in different NLP tasks. We open-source our dataset creation pipeline, instruction datasets, trained models, and evaluation outputs to promote language-specific studies on these models.