Blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) is conventionally done by reconstructing T(2)(*)-weighted images. However, since the images are unitless they are nonquantifiable in terms of important physiological parameters. An alternative approach is to reconstruct R(2)(*) maps which are quantifiable and have comparable BOLD contrast as T(2)(*)-weighted images. However, conventional R(2)(*) mapping involves long readouts and ignores relaxation during readout. Another problem with fMRI imaging is temporal drift/fluctuations in off-resonance. Conventionally, a field map is collected at the start of the fMRI study to correct for off-resonance, ignoring any temporal changes. Here, we propose a new fast regularized iterative algorithm that jointly reconstructs R(2)(*) and field maps for all time frames in fMRI data. To accelerate the algorithm we linearize the MR signal model, enabling the use of fast regularized iterative reconstruction methods. The regularizer was designed to account for the different resolution properties of both R(2)(*) and field maps and provide uniform spatial resolution. For fMRI data with the same temporal frame rate as data collected for T(2)(*)-weighted imaging the resulting R(2)(*) maps performed comparably to T(2)(*)-weighted images in activation detection while also correcting for spatially global and local temporal changes in off-resonance.