Abstract We consider the formation of molecules in primordial prestellar clumps and evaluate the line luminosities to assess detectability by next-generation observational facilities. If the initial $\mathrm{H}_2$ fraction is sufficiently high, HD becomes an important coolant in the clumps. The luminosity from such HD cooling clumps is lower than that from $\mathrm{H}_2$ cooling ones because of the lower temperature ($<100 \,\mathrm{K}$). As for Li reactions, we include the three-body LiH formation approximately. The Li molecular fraction remains very low ($<10^{-3}$) throughout the evolution, owing to the high dissociative reaction rate of $\mathrm{LiH} + \mathrm{H} \rightarrow \mathrm{Li} + \mathrm{H}_2$. LiH does not become an important coolant in any density range. The luminous emission lines from the prestellar cores include $\mathrm{H}_2$ rovibrational lines [1–0 Q(1), 1–0 O(3), 1–0 O(5)] and pure rotational lines [0–0 S(3), 0–0 S(4), 0–0 S(5)]. The next-generation facilities SPICA and JWST are able to detect $\mathrm{H}_2$ emission in a large pre-galactic cloud that forms metal-free stars at a high rate of $\sim 10^3 \,{{{M}_{\odot}}} \,\mathrm{yr}^{-1}$ at a redshift of $z < 10$. We also derive an analytical expression for the luminosity that reproduces the numerical results.