  We present new period-luminosity and period-luminosity-metallicity relations
for Galactic RR Lyrae stars based on a sample of 28 pulsators located at
distances up to $1.5$ kpc from the Sun. Near-infrared photometry was obtained
at the Cerro Armazones Observatory and parallaxes were taken from the Gaia
Early Data Release 3. Relations were determined for the 2MASS $JHK_s$ bands and
the $W_{JK}$ Wesenheit index. We compare our results with other calibrations
available in the literature and obtain very good agreement with the photometry
of RR Lyraes from the Large Magellanic Cloud anchored using the distance to the
Cloud, which based on detached eclipsing binaries. We find that the dependence
of absolute magnitudes on metallicity of $0.070\pm 0.042$ mag/dex ($J-$ band)
to $0.087 \pm 0.031$ mag/dex ($W_{JK}$ index) for the population of fundamental
pulsators (RRab) that is in agreement with previously published
phenomenological works. We perform a refined determination of distance to the
LMC based on our new calibration and photometry from Szewczyk et al. (2008). We
study the dependence of the fitted parameters of fiducial relations and the LMC
distance on the systematic parallax offset.
