We have demonstrated optical frequency combs (OFCs) featuring low and continuously tunable line spacing in the kilohertz range. The OFCs are generated by pulsed gain-switching of optically injected commercial semiconductor lasers emitting at around 1.55 μm. After generation, the OFCs are efficiently densified by pseudo-random-binary-sequence phase modulation. The case of an OFC generated by gain-switching at a repetition rate of 1 GHz has been numerically and experimentally analyzed and the conditions for optimal densification have been found. In this case, the comb has been densified by a factor of 2047 and exhibits a 90 GHz flat and broad spectrum consisting of more than 184,000 spectral lines, separated 488 kHz. Although this densification factor is not the largest that can be achieved with the method, it is more than 100 times larger than previously reported factors for gain-switching OFCs. These results open prospects for the use of potentially integrable gain-switching OFCs in applications requiring sub-megahertz line spacing. •Dense and broad-band OFCs in pulsed gain-switched optically injected semiconductor lasers.•Continuously tunable line spacing OFCs in the kilohertz range by PRBS phase modulation.•OFCs densified by 2047 with > 184,000 spectral lines separated 488 kHz were attained.•These results open prospects for the use of potentially integrable gain switching OFCs in applications requiring sub-megahertz line spacing.