The cross sections for e(+)e(-) -> phi pi(+)pi(-) and e(+)e(-) -> phi f(0)(980) are measured from threshold to root s = 3.0 GeV using initial-state radiation. The analysis is based on a data sample of 673 fb(-1) collected on and below the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. First measurements are reported for the resonance parameters of the phi(1680) in the phi pi(+)pi(-) mode: m = (1689 +/- 7 +/- 10) MeV/c(2) and Gamma = (211 +/- 14 +/- 19) MeV/c(2). A structure at root s = 2.1 GeV/c(2), corresponding to the so called Y(2175), is observed; its mass and width are determined to be (2079 +/- 13(-28)(+79)) MeV/c(2) and (192 +/- 23(-61)(+25)) MeV/c(2), respectively.