Using the OVRO, Nobeyama, and IRAM mm-arrays, we searched for ``disk-outflow systems in three high-mass (proto)star forming regions: G16.59-0.05, G23.01-0.41, and G28.87+0.07. These were selected from a sample of NH3 cores associated with OH and H2O maser emission and with no or very faint continuum emission. Our imaging of molecular line (including rotational transitions of CH3CN and 3mm dust continuum emission revealed that these are compact, massive, and hot molecular cores (HMCs), that is likely sites of high-mass star formation prior to the appearance of UCHII regions. All three sources turn out to be associated with molecular outflows from CO and/or HCO+ J=1--0 line imaging. In addition, velocity gradients of 10 -- 100 km/s per pc in the innermost densest regions of the G23.01 and G28.87 HMCs are identified along directions roughly perpendicular to the axes of the corresponding outflows. All the results suggest that these cores might be rotating about the outflow axis, although the contribution of rotation to gravitational equilibrium of the HMCs appears to be negligible. Our analysis indicates that the 3 HMCs are close to virial equilibrium due to turbulent pressure support. Comparison with other similar objects where rotating toroids have been identified so far shows that in our case rotation appears to be much less prominent; this can be explained by the combined effect of unfavorable projection, large distance, and limited angular resolution with the current interferometers.