In this paper we report on the Markarian 501 results obtained during our TeV $gamma$-ray observations from March 11 to May 12, 2005 and February 28 to May 7, 2006 for 112.5 hours with the TACTIC $gamma$-ray telescope. During 2005 observations for 45.7 hours, the source was found to be in a low state and we have placed an upper limit of 4.62 $times$ 10$^{-12}$ photons cm$^{-2}$ s$^{-1}$ at 3$sigma$ level on the integrated TeV $gamma$-ray flux above 1 TeV from the source direction. However, during the 2006 observations for 66.8h, detailed data analysis revealed the presence of a TeV $gamma$-ray signal from the source with a statistical significance of 7.5$sigma$ above $E_{gamma}geq$ 1 TeV. The time averaged differential energy spectrum of the source in the energy range 1-11 TeV is found to match well with the power law function of the form ($dPhi/dE=f_0 E^{-Gamma}$) with $f_0=(1.66pm0.52)times 10^{-11}cm^{-2}s^{-1}TeV^{-1}$ and $Gamma=2.80pm0.27$.
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