We demonstrate a compact fibre-based laser system at 2.05 microns stabilized to a CO2 transition using frequency modulation spectroscopy of a gas-filled hollow-core fibre. The laser exhibits an absolute frequency accuracy of 5 MHz, a frequency stability noise floor of better than 7 kHz or 5 × 10-11 and is tunable within ±200 MHz from the molecular resonance frequency while retaining roughly this stability and accuracy.