The exclusive production cross sections for omega and phi mesons have been
measured in proton-proton reactions at p(lab) = 3.67 CeV/c. The observed ph
i/omega cross section ratio is (3.8 +/- 0.2(-0.9)(+1.2)) x 10(-3). After ph
ase space corrections, this ratio is enhanced by about an order of magnitud
e relative to naive predictions based upon the Okubo-Zweig-Iizuka (OZI) rul
e, in comparison to an enhancement by a factor similar to 3 previously obse
rved at higher beam momenta. The modest increase of this enhancement near t
he production threshold is compared to the much larger increase of the phi/
omega ratio observed in specific channels of (p) over barp annihilation exp
eriments. Furthermore, differential cross section results are also presente
d which indicate that although the phi meson is predominantly produced from
a P-3(1) proton-proton entrance channel, other partial waves contribute si
gnificantly to the production mechanism at this beam momentum.