Scanning tunneling microscopy has been used to study the surface morphology of strained In1-xGaxAs layers (either 2% compressively or 2% tensilely strained for x=0.18 or x=0.75, respectively) grown by molecular beam epitaxy on (001) InP substrate under cation-stabilized conditions. Under such growing conditions a smooth two-dimensional (2D) surface morphology is well preserved until the onset of plastic relaxation. This behavior is completely unlike the 2D/3D growth mode transition observed under As-stabilized conditions of growth. Along with the 2D growth mode stabilization, a step-edge smoothing is also observed. These results are assigned to a high value of step formation free energy on (4x2) reconstructed surfaces. The resultant increase in surface tension delays the onset of coherent 3D island formation beyond the onset of plastic relaxation and stabilizes 2D growth.