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The Ξ_{c}^{+}π^{-}π^{+} spectrum is investigated using proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb^{-1}, collected by the LHCb experiment during 2016-2018. Four states are observed with high significance, and their masses and widths are measured to be m[Ξ_{c}(2815)^{+}]=2816.65±0.03±0.03±0.23 MeV, Γ[Ξ_{c}(2815)^{+}]=2.07±0.08±0.12 MeV, m[Ξ_{c}(2923)^{+}]=2922.8±0.3±0.5±0.2 MeV, Γ[Ξ_{c}(2923)^{+}]=5.3±0.9±1.4 MeV, m[Ξ_{c}(2970)^{+}]=2968.6±0.5±0.5±0.2 MeV, Γ[Ξ_{c}(2970)^{+}]=31.7±1.7±1.9 MeV, [Ξ_{c}(3080)^{+}]=3076.8±0.7±1.3±0.2 MeV, Γ[Ξ_{c}(3080)^{+}]=6.8±2.3±0.9 MeV, where the uncertainties are statistical, systematic, and due to the limited precision on the Ξ_{c}^{+} mass, respectively. The Ξ_{c}(2923)^{+} baryon is observed for the first time, and is consistent with being the isospin partner of the previously observed Ξ_{c}(2923)^{0} state. Most of the measured parameters are more precise than existing world averages.