An enhancement near threshold is observed in the omega(phi) invariant mass spectrum from the doubly Okubo-Zweig-Iizuka-suppressed decays of J/psi-->gamma(omega)phi, based on a sample of 5.8 x 10(7) J/psi events collected with the BESII detector. A partial wave analysis shows that this enhancement favors JP=0+, and its mass and width are M=1812(+19)(-26)(stat)+/-18(syst) MeV/c2 and Gamma=105+/-20(stat)+/-28(syst) MeV/c2. The product branching fraction is determined to be B(J/psi-->gammaX)B(X-->omega(phi))=[2.61+/-0.27(stat)+/-0.65(syst)]x10(-4).

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