We present measurements of two-particle correlations with neutral pion trigger particles of transverse momenta 8 < pT < 16 GeV/c and associated charged particles of 0.5 < pT < 10 GeV/c versus the azimuthal angle difference Δφ at midrapidity in pp and central Pb–Pb collisions at √sNN = 2.76 TeV with ALICE. The new measurements exploit associated charged hadrons down to 0.5 GeV/c, which significantly extends our previous measurement that only used charged hadrons above 3 GeV/c. After subtracting the contributions of the flow background, v2 to v5, the per-trigger yields are extracted for |Δφ|<0.7 on the near and for | Δφ−π|<1.1 on the away side. The ratio of per- trigger yields in Pb–Pb to those in pp collisions, IAA, is measured on the near and away side for the 0–10% most central Pb–Pb collisions. On the away side, the per-trigger yields in Pb–Pb are strongly suppressed to the level of IAA≈0.6 for pT(assoc) > 3 GeV/c, while with decreasing momenta an enhancement develops reaching about 5 at low pT(assoc). On the near side, an enhancement of IAA between 1.2 at the highest to 1.8 at the lowest pT(assoc) is observed. The data are compared to parton-energy- loss predictions of the JEWEL and AMPT event generators, as well as to a perturbative QCD calculation with medium- modified fragmentation functions. All calculations qualitatively describe the away-side suppression at high pT(assoc). Only AMPT captures the enhancement at low pT(assoc), both on the near and away side. However, it also underpredicts IAA above 5 GeV/c, in particular on the near-side.