Germanium(001) surfaces deposited with less than 0.3nm thick Ag on average were studied by scanning tunneling microscopy. After the small amount of Ag deposition at 100K, thin two-dimensional (2D) islands with 0.18nm height are predominantly found to elongate to the dimer-row direction on clean Ge(001)-2x1 surfaces. With increasing temperature during the deposition, the density of three dimensional (3D) islands with more than 0.6nm height increases, although few 2D islands are still formed at room temperature. With increasing average thickness of deposited Ag, the density of 3D islands increases at any temperature between 100K and 300K. These features are explained in terms of the diffusion of Ag atoms on the surface during deposition.