ROSAT X-ray images and spectra of the inner parts of the Virgo cluster around M87 are presented and compared with a new deep radio map. Apart from the emission peaked on M87, a roughly linear structure, noted previously by Feigelson et al. using Einstein Observatory data and correlated with the outer radio halo, is seen. We have carried out the first spectral analysis of this structure and find that it is clearly due to thermal emission from metal-rich gas at a temperature significantly lower than that of the surrounding intracluster gas. We propose several models to account for the enhanced X-ray emissivity in the radio halo.