We present new results of the HESS J1731-347/SNR G353.6-0.7 system from XMM-Newton and Suzaku X-ray observations and Delinha CO observations. We discover extended hard X-rays coincident with the bright, extended TeV source HESS J1731-347 and the shell of the radio supernova remnant (SNR). We find that spatially resolved X-ray spectra can generally be characterized by an absorbed power-law model, with a photon index of ∼2, typical of non-thermal emission. A bright X-ray compact source, XMMS J173203-344518, is also detected near the center of the SNR. We find no evidence of a radio counterpart or an extended X-ray morphology for this source, making it unlikely to be a pulsar wind nebular (PWN). The spectrum of the source can be well fitted by an absorbed blackbody with a temperature of ∼0.5 keV plus a power-law tail with a photon index of ∼5, reminiscent of the X-ray emission of a magnetar. CO observations toward the inner part of the High Energy Stereoscopic System (HESS) source reveal a bright cloud component at −20 ± 4 km s −1 , which is likely located at the same distance of ∼3.2 kpc as the SNR. Based on the probable association between the X-ray and γ -ray emissions and likely association between the CO cloud and the SNR, we argue that the extended TeV emission originates from the interaction between the SNR shock and the adjacent CO clouds rather than from a PWN.