The generation and propagation regulation of Airy solitons in saturable nonlinear medium are numerically investigated by split-step Fourier method. For a single incident Airy beam, stably propagated breathing solitons are generated within a certain initial amplitude range. The intensity of solitons increases and breathing period decreases with the increase of initial amplitude, but the solitons width remains unchanged. With the increase of decay coefficient, mean peak intensity of the solitons has two extreme values, and it is found to first increase, then decrease and increase again. Left tilted Airy solitons can be generated with a negative launch angle, and right tilted Airy solitons can be generated with a positive launch angle. When two incident Airy beams interact with each other, the interaction can be weakened with the same negative launch angles, and the interaction can be strengthened with the same positive launch angles. Furthermore, the propagation direction of solitons or soliton pairs can be controlled by different launch angles.