We present the second portion of an unbiased survey of the Galactic plane for 6668‐MHz methanol masers. This section of the survey spans the longitude range 6° to 20°. We report the detection of 119 maser sources, of which 42 are new discoveries. The masers are tightly constrained to the Galactic plane, with only four outside a latitude range of ±1°. This longitude region includes the brightest known 6668‐MHz methanol maser, 9.621+0.196, as well as the two brightest newly discovered sources in the southern survey as a whole. We list all the sources associated with the 3‐kpc arms within ±15° longitude and consider further candidates beyond 15° longitude. We identify three new sources associated with the Galactic bar and comment on the density of masers in relation to the bar orientation.