We present measurements of the top quark mass in ttbar candidate events with two final state leptons using 1 inverse fb of data collected by the D0 experiment. Our data sample is selected by requiring two fully identified leptons or by relaxing one lepton requirement to an isolated track if at least one jet is tagged as a b jet. The top quark mass is extracted after reconstructing the event kinematics under the ttbar hypothesis using two methods. In the first method, we integrate over expected neutrino rapidity distributions, and in the second we calculate a weight for the possible top quark masses based on the observed particle momenta and the known parton distribution functions. We analyze 83 candidate events in data and obtain m_t = 176.2 +/- 4.8 (stat) +/- 2.1 (sys) GeV and m_t = 173.2 +/- 4.9 (stat) +/- 2.0 (sys) GeV for the two methods, respectively. Accounting for correlations between the two methods, we combine the measurements to obtain m_t = 174.7 +/- 4.4 (stat) +/- 2.0 (sys) GeV.