After some time I managed to find a solution, though, I do not know exactly why it works.

The microscope I am using comes with small 2Mpx camera with it, and, lens that are to be attached to the camera and fitted onto the microscope. The radial blur disappeared after I took the fixed lens from the microscope camera, and fitted it onto my DSLR, using custom 3D printed adaptor T-ring.

Graphically this is how it looks:

After assembly:

Stl and f3d files for 3D printing the ring are available here. Though, my case was very special, that is to say, I had to do a lot of guesswork in post-processing to make the ring work. So you may want to tweak the model for your equipment, even design it all from scratch.

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A tip for you to try if you are dealing with similar problems is to try something called Köhler Illumination. Köhler Illumination is a technique for adjusting the light source and apperture of the microscope in order to achieve the best light possible. In my particular case, setting up Köhler helped a lot, though it did not solve problem completely. Tips on setting up Köhler Illumination and microphothography in general.

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Note: Since I am using lens that came packed in with the microscope, the DSLR does not automatically apply the lens correction to the image. For this problem I found using Photoshop lens correction feature very useful.