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In the presence of an applied axial magnetic field Ha the uniaxial antiferromagnets FeCl2 and FeBr2 show fluctuating domain-like antiferromagnetic correlations above the phase boundary Tc(Ha). They are detected by SQUID measurements of the low frequency out-of-phase susceptibility gc″ and indicate a field-induced Griffiths phase at temperatures Tc(Ha) < T < TN. In contrast to FeCl2, important additional frustration-induced intraplanar non-critical contributions to χ″ vs. T are found in FeBr2. For external fields above the Tc(Ha) line, Ha > 2.6 MA/m, they are shown to superimpose linearly on the Griffiths contributions. These dominate at Ha = 2.67 MA/m and are unequivocally modeled within the Landau theory of fluctuations near phase transitions by introducing a Lorentzian Tc distribution.