Which authority establishes the equivalence of degrees from different European countries? I hold a degree from a European country, and at that time we didn't have a system similar to the common "Bachelor +  Master". My degree has been considered as equivalent to a Master by the University of another European country, and in this other University I obtained a Doctorate.

Now, I have been offered a teaching position in Russia, and they want a statement of my undergraduate University, saying that that degree is equivalent to a Master. But this University (where I graduated) tells me that they can't make a statement of equivalence, they can only certify that I have that degree.
So, who should be the authority that officially takes care of confirming the equivalence?

To complicate things, I graduated before the Bologna Process came into effect.
Each country should have a government office (or equivalent organization) that makes such determinations. You should ask the university to which you're applying for the appropriate office to consult in their country. If you want one from the country where you obtained your undergraduate degree, ask their registrar (or equivalent officer) who is responsible for such certifications.