We present measurements of two-particle correlations with neutral pion trigger particles of transverse momenta 8>pT trig>16 GeV/c and associated charged particles of 0.5>pT assoc>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.