Searches for pair production of supersymmetric particles under the assumption that R-parity is not conserved are presented, based on data recorded by the DELPHI detector in 1998 from e+e- collisions at a centre-of-mass energy of 189 GeV. Only one R-parity violating LL\bar{E} term (i.e. one lambda coupling), which couples scalar leptons to leptons, is considered to be dominant at a time. Moreover, it is assumed that the strength of the R-parity violating couplings is such that the lifetimes can be neglected. The search for pair production of neutralinos, charginos and sleptons has been performed for both direct R-parity violating decays and indirect cascade decays. The results are in agreement with Standard Model expectations, and are used to update the constraints on the MSSM parameter values and the mass limits previously derived at sqrt(s) = 183 GeV. The present 95% C.L. limits on supersymmetric particle masses are: m_{\tilde{\chi}^0} > 30 GeV/c^2 and m_{\tilde{\chi}^\pm} > 94 GeV/c^2; m_{\tilde{\nu}} > 76.5 GeV/c^2 (direct and indirect decays); m_{\tilde{\ell}_R} > 83 GeV/c^2 (indirect decay only).