Muon spin rotation/relaxation (μSR) and polar Kerr effect measurements provide evidence for a time-reversal symmetry breaking (TRSB) superconducting state in Sr₂RuO₄. However, the absence of a cusp in the superconducting transition temperature (T_c) vs stress and the absence of a resolvable specific heat anomaly at TRSBtransition temperature (T_TRSB) under uniaxial stress challenge a hypothesis of TRSB superconductivity. Recent μSR studies under pressure and with disorder indicate that the splitting between T_c and T_TRSB occurs only when the structural tetragonal symmetry is broken. To further test such behavior, we measured T_c through susceptibility measurements and T_TRSB through μSR, under uniaxial stress applied along a ⟨110⟩ lattice direction. We have obtained preliminary evidence for suppression of T_TRSB below T_c, at a rate much higher than the suppression rate of T_c.