We investigate low-energy modes of the 6 Li( 3 He, p) nuclear reaction leading to a production of 8 Be nuclei in 16.63 and 16.92 MeV excited states which may have important applications in nuclear fusion research. An extrapolation procedure developed previously is used to calculate reaction cross sections σ at energies below 1 MeV and the corresponding Maxwellian rate parameters σ v in the 0-200 keV temperature range. A significant discrepancy between the present values of σ v and those accepted elsewhere is marked at low temperatures. An effect of low-energy resonances associated with highly excited states in the compound nucleus 9 B is discussed. The calculated 6 Li + 3 He reaction cross sections and rate parameters are tabulated.