In this paper we report on the Markarian 501 results obtained during our TeV γ-ray observations from 11 March to 12 May 2005 and 28 February to 7 May 2006 for 112.5 h with the TACTIC γ-ray telescope. During 2005 observations for 45.7 h, the source was found to be in a low state and we have placed an upper limit of 4.62 × 10⁻¹² photons cm⁻² s⁻¹ at 3σ level on the integrated TeV γ-ray flux above 1 TeV from the source direction. However, during 2006 observations for 66.8 h, detailed data analysis revealed the presence of a TeV γ-ray signal from the source with a statistical significance of 7.5σ above E_γ≥ 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 (dΦ/dE = f₀E^−Γ) with f₀ = (1.66 ± 0.52) × 10⁻¹¹ cm⁻² s⁻¹ TeV⁻¹ and Γ = 2.80 ± 0.27.