Earthquake early warning (EEW) systems aim to provide advance warnings of impending strong ground shaking. Many EEW systems are based on a strategy in which precise and rapid estimates of source parameters, such as hypocentral location and moment magnitude (), are used in a ground‐motion prediction equation (GMPE) to predict the strength of ground motion. For large earthquakes with long rupture duration, the process is repeated, and the prediction is updated in accordance with the growth of during the ongoing rupture. However, in some regions near the causative fault this approach leads to late warnings, because strong ground motions often occur during earthquake ruptures before can be confirmed. increases monotonically with elapsed time and reaches its maximum at the end of rupture, and ground motion predicted by a GMPE similarly reaches its maximum at the end of rupture, but actual generation of strong motion is earlier than the end of rupture. A time gap between maximum and strong‐motion generation is the first factor contributing to late warnings. Because this time gap exists at any point of time during the rupture, a late warning is inherently caused even when the growth of can be monitored in real time. In the near‐fault region, a weak subevent can be the main contributor to strong ground motion at a site if the distance from the subevent to the site is small. A contribution from a weaker but nearby subevent early in the rupture is the second factor contributing to late warnings. Thus, an EEW strategy based on rapid estimation of is not suitable for near‐fault regions where strong shaking is usually recorded. Real‐time monitoring of ground motion provides direct information for real‐time prediction for these near‐fault locations.