Aims: We present multiwavelength observations of one of the most distant gamma-ray bursts detected so far, GRB 080913. Based on these observations, we consider whether it could be classified as a short-duration GRB and discuss the implications for the progenitor nature and energy extraction mechanisms. Methods: Multiwavelength X-ray, near IR and millimetre observations were made between 20.7 hours and 16.8 days after the event. Results: Whereas a very faint afterglow was seen at the 3.5m CAHA telescope in the nIR, the X-ray afterglow was clearly detected in both Swift and XMM-Newton observations. An upper limit is reported in the mm range. We have modeled the data assuming a collimated $theta_0$ $gtrsim$ 3$^circ$ blast wave with an energy injection at 0.5 days carrying $5sim 10^{52}$ erg or approximately 12 times the initial energy of the blast wave. We find that GRB 080913 shares many of the gamma-ray diagnostics with the more recent burst GRB 090423 for being classified as short had they ocurred at low redshift. If the progenitor were a compact binary merger, it is likely composed by a NS and BH. The Blandford-Znajek (BZ) mechanism is the preferred one to extract energy from the central, maximally-rotating BH. Both the magnetic field close to the event horizon (B) and the BH mass ($M_{bh}$) are restricted within a relatively narrow range, such that $(B / 3times 10^{16} rm{G}) (M_{bh} / 7 M_odot) sim 1$. Similar constraints on the central BH hold for collapsar-like progenitor systems if the BZ-mechanism works for the system at hand.
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