Context : In the last years , the persistent source 1E 1743.1–2843 has been observed in the X-rays , but never above 20 keV . In previous works , it was stressed that a possible high energy emission could give further indications on the accreting object nature which remains still unknown . Aims : We present here more than two years of 1E 1743.1–2843 monitoring with INTEGRAL /IBIS as well as public XMM-Newton and Chandra X-ray observations . Methods : The temporal study in the 20–40 keV band shows a rather constant flux on few months time scale . Based on this result we have performed the broad-band spectral analysis using EPIC/IBIS non simultaneous data and ACIS-I/IBIS data collected during 2004 . Results : In \sim 2 Ms , we report a detection of 6 \sigma in the energy range 35–70 keV . The first broad-band study ( 2–70 keV ) shows a steep slope ( \sim 3 ) and a black body temperature of 1.7 keV . Conclusions : Combining spectral parameters and discussion about the luminosity evaluations for different possible distances , our conclusions are in favour of a LMXB system with a neutron star at distance higher than the Galactic Centre , even though a firm conclusion can not be stated .