The disparity in language resources poses a challenge in multilingual NLP, with high-resource languages benefiting from extensive data, while low-resource languages lack sufficient data for effective training. Our Contrastive Language Alignment with Prompting (CoLAP) method addresses this gap by integrating contrastive learning with cross-lingual representations, facilitating task-specific knowledge transfer from high-resource to lower-resource languages. The primary advantage of our approach is its data efficiency, enabling rapid adaptation to new languages and reducing the need for large labeled datasets. We conduct experiments with multilingual encoder-only and decoder-only language models on natural language understanding tasks, including natural language inference and relation extraction, evaluating performance across both high- and low-resource languages. Our results demonstrate that CoLAP outperforms few-shot cross-lingual transfer baselines and in-context learning, even with limited available data. This effectively narrows the cross-lingual performance gap, contributing to the development of more efficient multilingual NLP techniques.