This study develops autonomous manipulation strategies for a mobile untethered microrobot that operates on a 2-D surface in a fluidic environment. The microrobot, which is a permanent magnet, is under m in all dimensions and is actuated by oscillating external magnetic fields. Two types of manipulations are considered: 1) front pushing, where the microrobot pushes a micro-object by direct contact; and 2) side pushing, which can result in noncontact pushing, where the fluid flow fields that are generated by a translating microrobot are used to displace a micro-object. Physical models are provided to estimate the displacement of the micro-object due to the fluid motion. Model-based controllers to perform contact and noncontact manipulation are proposed, which iteratively correct emerging manipulation behaviors to improve performance. It is found that using a model-based solution as a feed-forward input, which is combined with a learning controller, can significantly improve micro-object pushing performance. Finally, we begin to address the problem to assemble two micro-objects together using the microrobot, which is only successful by using a side-pushing method.