Results on two-particle angular correlations for charged particles produced in pp collisions at a center-of- mass energy of 13 TeV are presented. The data were taken with the CMS detector at the LHC and correspond to an integrated luminosity of about 270 nb(-1). The correlations are studied over a broad range of pseudorapidity (vertical bar eta vertical bar < 2.4) and over the full azimuth (phi) as a function of charged particle multiplicity and transverse momentum (p(T)). In high-multiplicity events, a long-range (vertical bar Delta eta vertical bar > 2.0), near-side (Delta phi approximate to 0) structure emerges in the two-particle Delta eta-Delta phi correlation functions. The magnitude of the correlation exhibits a pronounced maximum in the range 1.0 < p(T) < 2.0 GeV/c and an approximately linear increase with the charged particle multiplicity, with an overall correlation strength similar to that found in earlier pp data at root s = 7 TeV. The present measurement extends the study of near-side long-range correlations up to charged particle multiplicities N-ch similar to 180, a region so far unexplored in pp collisions. The observed longrange correlations are compared to those seen in pp, pPb, and PbPb collisions at lower collision energies.