Inclusive production cross sections are measured in deep inelastic scattering at HERA for meson states composed of a charm quark and a light antiquark or the charge conjugate. The measurements cover the kinematic region of photon virtuality 2 < Q2 < 100 GeV2, inelasticity 0.05 < y < 0.7, D meson transverse momenta pt(D) ≥ 2.5 GeV and pseudorapidity |η(D)| ≤ 1.5. The identification of the D-meson decays and the reduction of the combinatorial background profit from the reconstruction of displaced secondary vertices by means of the H1 silicon vertex detector. The production of charmed mesons containing the light quarks u, d and s is found to be compatible with a description in which the hard scattering is followed by a factorisable and universal hadronisation process.