Using 2.92 fb-1 of electron-positron annihilation data collected at a center-of-mass energy of sort(s)=3.773 GeV with the BESIII detector, we present an improved measurement of the branching fraction B(D+-->omega e+nu_e)=(1.63±0.11±0.08)x10-3. The parameters defining the corresponding hadronic form factor ratios at zero momentum transfer are determined for the first time; we measure them to be rV=1.24±0.09±0.06 and r2=1.06±0.15±0.05. The first and second uncertainties are statistical and systematic, respectively. We also search for the decay D+-->phi e+nu_e. An improved upper limit B(D+-->phi e+nu_e)<1.3x10-5 is set at 90% confidence level.
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