BAGRAM, Afghanistan — Military commanders with the NATO mission in Afghanistan told President Barack Obama's chief envoy to the region this weekend that they did not have enough troops to do their job, pushed past their limit by Taliban rebels who operated across borders.

The commanders emphasized problems in southern Afghanistan, where Taliban insurgents continue to bombard towns and villages with rockets despite a new influx of U.S. troops, and in eastern Afghanistan, where the father-and-son-led Haqqani network of militants has become the main source of attacks against U.S. soldiers and their Afghan allies.....