Using scanning tunneling microscopy, we studied Ge(001) surfaces covered with an average of approximately 0.8 monolayers of silver. In the deposition at room temperature, we observed that Ag predominantly grew in a three-dimensional (3D) mode on bare Ge substrates, corresponding to Volmer-Weber growth. At the same time, we found two-dimensional (2D) Ag islands elongated in the dimer-row direction with one monolayer height, though the density of the 2D islands was smaller than one-fifth of that of the 3D islands. Images with atomic resolution showed stripe patterns on the 2D islands and enhancement of asymmetry of the Ge dimers on both sides of the islands at high positive bias voltages.