If you don’t need to recover high-frequency information along the K axis (it is enough to smoothly interpolate along the slices) then you have a couple of simple options.
A. Anti-aliasing filter on the image. You can use a windowed sinc kernel, with strong smoothing along the K axis and no smoothing along I and J axes.
B. Compute signed distance map and threshold that. This is implemented in the resample module in BRAINSTools.
C. Convert the labelmap to closed surface, apply low-pass filter on the surface (for example, using vtkWindowedSincPolyDataFilter), then convert back to labelmap.
D. Insert empty slices between the segmented slices and run ITKMorphologicalContourInterpolation filter to smoothly interpolate between them.
You can try all these options using Python scripting using ITK and VTK classes, or by a couple of clicks using the GUI of 3D Slicer.