We compute the probability that intermediate mass black holes (IMBHs) capture companions due to dynamical interactions and become accreting sources, and explore the possibility that the accreting IMBHs would appear as ultra-luminous X-ray sources (ULXs). We focus on IMBHs originating from low-metallicity Population III stars. Two channels of IMBH formation are considered: from primordial halos in the framework of hierarchical clustering, and from non-mixed, zero-metallicity primeval gas in galactic discs. IMBHs can form binary systems due to tidal captures of single stars and exchange interactions with existing binary systems in galactic discs. We find that neither formation mechanism of the accreting IMBH binary is able to provide enough sources to explain the observed population of ULXs. Even at sub-ULX luminosity, the total number of accreting IMBHs with $L> 10^{36}$ erg s$^{-1}$ with dynamically captured companions is found to be $< 0.01$ per galaxy.

21 pages, 5 figures. Accepted to MNRAS