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We present here medium resolution (λ/Δλ ∼ 1200) H- and K-band spectra of M-type dwarf stars covering the wavelength ranges 1.50-1.80 µm and 1.95-2.45 µm. The sample includes 53 dwarf stars (M0V-M7V) from new observations using the TIFR Near-Infrared Spectrometer and Imager instrument on the 2-m Himalayan Chandra Telescope. Using interferometrically measured effective temperature (T_eff), radius and luminosity of nearby bright calibrator stars, we have created new empirical relationships among those fundamental parameters and spectral indices. The equivalent widths of H-band spectral features like Mg (1.57 µm), Al (1.67 µm) and Mg (1.71 µm), and the H₂O-H index are found to be good indicators of T_eff, radius and luminosity and we establish linear functions using these features relating to those stellar parameters. The root-mean-squared error of our best fits are 102 K, 0.027 R_☉ and 0.12 dex respectively. Using spectral-type standards along with known parallaxes, we calibrate both H- and K-band H₂O indices as a tracer of spectral type and absolute K_s magnitude. Metallicities of M-dwarf samples are estimated using the K-band calibration relationships. The masses of M dwarfs could be determined using the luminosity (L/ L_☉_) and we establish a new empirical relation for this. We also compare and contrast our results with other similar work from the literature.