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Strange particle production in A+A interactions at 158 AGeV is studied by the CERN experiment NA49 as a function of system size and collision geometry. Yields of charged kaons, phi and Lambda are measured and compared to those of pions in central C+C, Si+Si and centrality-selected Pb+Pb reactions. An overall increase of relative strangeness production with the size of the system is observed which does not scale with the number of participants. Arguing that rescattering of secondaries plays a minor role in small systems the observed strangeness enhancement can be related to the space-time density of the primary nucleon-nucleon collisions.