Polarization dependent ground state absorption, excited state absorption and emission cross sections of Pr, Mg:SrAl12O19 are determined in the visible and ultraviolet spectral region. It is shown that excited state absorption to the 4f5d configuration does neither occur on the pump wavelength in the blue region nor on any of the visible laser transitions. Efficient laser action at 643.5 nm is demonstrated with slope efficiencies of up to 47% with respect to the absorbed pump power. Output powers up to 75 mW are achieved by pumping with an InGaN laser diode at 444 nm.