Cortical connectivity mostly stems from local axonal arborizations, suggesting coordination is strongest between nearby neurons in the range of a few hundred micrometers. Yet multi-electrode recordings of resting-state activity in macaque motor cortex show strong positive and negative spike-count covariances between neurons that are millimeters apart. Here we show that such covariance patterns naturally arise in balanced network models operating close to an instability where neurons interact via indirect connections, giving rise to long-range correlations despite short-range connections. A quantitative theory explains the observed shallow exponential decay of the width of the covariance distribution at long distances. Long-range cooperation via this mechanism is not imprinted in specific connectivity structures but rather results dynamically from the network state. As a consequence, neuronal coordination patterns are not static but can change in a state-dependent manner, which we demonstrate by comparing different behavioral epochs of a reach-to-grasp experiment.