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 (|η|<2.4) and over the full azimuth (ϕ) as a function of charged particle multiplicity and transverse momentum (p_{T}). In high-multiplicity events, a long-range (|Δη|>2.0), near-side (Δϕ≈0) structure emerges in the two-particle Δη-Δϕ 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 sqrt[s]=7 TeV. The present measurement extends the study of near-side long-range correlations up to charged particle multiplicities N_{ch}∼180, a region so far unexplored in pp collisions. The observed long-range correlations are compared to those seen in pp, pPb, and PbPb collisions at lower collision energies.