Context. The surface layers of the Sun are strongly stratified. In the presence of turbulence with a weak mean magnetic field, a large-scale instability resulting in the formation of nonuniform magnetic structures, can be excited on the scale of many (more than ten) turbulent eddies (or convection cells). This instability is caused by a negative contribution of turbulence to the effective (mean-field) magnetic pressure and has previously been discussed in connection with the formation of active regions. Aims: We want to understand the effects of rotation on this instability in both two and three dimensions. Methods: We use mean-field magnetohydrodynamics in a parameter regime in which the properties of the negative effective magnetic pressure instability have previously been found to agree with properties of direct numerical simulations. Results: We find that the instability is already suppressed for relatively slow rotation with Coriolis numbers (i.e. inverse Rossby numbers) around 0.2. The suppression is strongest at the equator. In the nonlinear regime, we find traveling wave solutions with propagation in the prograde direction at the equator with additional poleward migration away from the equator. Conclusions: We speculate that the prograde rotation of the magnetic pattern near the equator might be a possible explanation for the faster rotation speed of magnetic tracers relative to the plasma velocity on the Sun. In the bulk of the domain, kinetic and current helicities are negative in the northern hemisphere and positive in the southern.