  Molecular hydrogen line radiation emitted in formation events of
first-generation stars are evaluated in a discussion of its detectability by
future observational facilities. H_2 luminosity evolution from the onset of
prestellar collapse until the formation of a \sim 100 M_{\odot} protostar is
followed. Calculations are extended not only to the early phase of the runaway
collapse but also to the later phase of accretion, whose observational features
have not been studied before. Contrary to the runaway collapse phase, where the
pure-rotational lines are always dominant, in the accretion phase rovibrational
line emission becomes prominent. The maximum luminosity is also attained in the
accretion phase for strong emission lines. The peak intensity of the strongest
rovibrational line reaches \sim 10^{-29} (W/m^2), corresponding to the flux
density of 10^{-5} (\mu Jy), for a source at the typical redshift of
first-generation star formation, 1+z=20. Although the redshifted rovibrational
H_2 emission from such an epoch falls in the wavelength range of the
next-generation infrared satellite, Space Infrared Telescope for Cosmology and
Astrophysics, for exceeding the detection threshold 10^7 such protostars are
required to reach the maximum luminosity simultaneously in a pregalactic cloud.
It is improbable that this condition is satisfied in a realistic scenario of
early structure formation.
