We present the results of an XMM-Newton observation of the slowly rotating (P = 3.4 s), highly magnetized (B ≈ 3 × 10¹³ G) radio pulsar PSR J0726–2612. A previous X-ray observation with the Chandra satellite showed that some of the properties of PSR J0726–2612 are similar to those of the X-ray-dim isolated neutron stars (XDINSs), a small class of nearby slow pulsars characterized by purely thermal X-ray spectra and undetected in the radio band. We confirm the thermal nature of the X-ray emission of PSR J0726–2612, which can be fitted by the sum of two blackbodies with temperatures kT₁=0.074^+0.006_-0.011 keV and kT₂=0.14^+0.004_-0.002 keV and emitting radii R₁=10.4^+10.8_-2.8 km and R₂=0.5^+0.9_-0.3 km, respectively (assuming a distance of 1 kpc). A broad absorption line modeled with a Gaussian profile centered at 0.39^+0.02_-0.03 keV is required in the fit. The pulse profile of PSR J0726–2612 is characterized by two peaks with similar intensity separated by two unequal minima, a shape and pulsed fraction that cannot be reproduced without invoking magnetic beaming of the X-ray emission. The presence of a single radio pulse suggests that in PSR J0726–2612 the angles that the dipole axis and the line of sight make with the rotation axis, ξ and χ, respectively, are similar. This geometry differs from that of the two radio-silent XDINSs with double-peaked pulse profiles similar to that of PSR J0726–2612, for which ξ ∼ 90° and χ ∼ 45° have recently been estimated. These results strengthen the similarity between PSR J0726–2612 and the XDINSs and support the possibility that the lack of radio emission from the latter might simply be due to an unfavorable viewing geometry.