A recent computation of the helium dimer interaction potential for intermediate distances (2 less than or equal to R/a(0) less than or equal to 15) using the (explicitly correlated) r(12)-MR-ACPF (averaged coupled-pair functional) method [GDANITZ, R. J., 1999, Molec. Phys., 96, 1423] is extended to larger basis sets. Calculations including a large atom centred [11s8p6d5f 4g3h2i1k] set show that the convergence of the energy with respect to enlargement of the basis set has previously been considerably underestimated. The extension of the P-k potential (292.75 +/- 0.01, 10.980 +/- 0.004 and -4.620 +/- 0.002 K at R = 4, 5.6 and 7 a(0)) to distances between 2.5 and 15 a(0) (P-k*) is close to a recent potential of van Mourik and Dunning [1999, J. Chem. Phys., 111, 9248] and it is believed to be the most accurate available. It gives rise to He-4(2) molecular constants of [R] = 46. 4 +/- 1.4 Angstrom and D-0 = 1.67 +/- 0.11 mK.