Allright, after some digging and experiments here the complex solution:
To avoid gaps between objects or graphics entities in a libGDX application one should:
1. ensure to use floats everywhere - even for storing target screen resolution, to avoid unwanted casts and following precision loss; OpenGL is using floats for positioning, so should you;
2. use power-of-two textures: those with side sizes aliquot to 2^x - 32x32, 16x64, 128x256 and so on; doing so will satisfy the minimization of memory usage on GPU and will help to avoid texture coordinates distortions due to float-int casts, that may or may not happen whithin the rendering process ( whatch for your shaders and datatypes );
3. use POT textures even if documentation says that you can do the opposite; POTs are great;
4. try to use NEAREST filtering for loaded textures and texture atlases; this would protect you from wrong 'pixel mix', when OpenGL will try to average your color-filled pixels with transparent ones; however, for me that showed no significant results;
5. hit your artist ensure that all of your full-frame graphics elements have no transparent or half-transparent pixels at the edges - sith happens, you now
6. use tight alignment and/or scale your objects just a little bit, so that they will overlay each other.
Hope that would help someone. Cheers.