Final answer:
The World Health Organization (WHO) is the UN agency responsible for promoting worldwide health and combating diseases through leadership in health matters, research shaping, and health monitoring.
Step-by-step explanation:
The UN agency that promotes worldwide health to combat the spread of diseases is the World Health Organization (WHO). This specialized agency of the United Nations is dedicated to global health issues. The WHO leads in providing necessary guidance on health-related matters, shapes the research agenda on health, and diligently monitors health situations, assessing health trends across the world. They offer essential information about the state of health, manage outbreak alerts, and update on current health news on their website.