Oceanic spreading, concurrent with Icelandic plume activity during the last 16 million years has created the Icelandic crust. The Tertiary Thverartindur central volcanic complex was located at the Icelandic spreading margin c. 5–7 Ma ago and reveals evidence for episodic magmatic activity. Intrusive rocks range from ultramafic through olivine- and quartz-tholeiitic gabbros and hybrid rocks to granitic rocks. The mafic intrusions form sill-like bodies with compositions close to those expected for magmatic liquids. Field evidence indicates that episodic emplacement of basaltic magma took place over a considerable time span and confirms the contemporaneous existence of primitive and more evolved mafic magmas. Granitic and ultramafic rocks represent the latest phase of magmatism at a spreading margin. The Thverartindur rocks are depleted in MgO, Ni and Cr, which is compatible with early fractionation of olivine and pyroxene. Calculated parental liquid for this complex is picritic (>18 wt% MgO) and resembles picritic lavas from the Reykjanes Peninsula and western Skye, and dykes from Rum and Mull. The compositions of the Thverartindur high-magnesian dykes, olivine- and quartz-tholeiitic gabbros, and granites can be modelled through decompressional fractional crystallization of this magma. The gabbroic sills are crystallized at low pressure following equilibrium crystallization paths.