Abridged: The Red MSX Source (RMS) survey is an ongoing multi-wavelength observational programme designed to return a large, well-selected sample of massive young stellar objects (MYSOs). Here we present 13CO observations made towards 854 MYSOs candidates located in the 3rd and 4th quadrants. We detected 13CO emission towards a total of 751 of the 854 RMS sources observed (~88%). In total 2185 emission components are detected above 3$sigma$ level. Multiple emission profiles are observed towards the majority of these sources - 455 sources (~60%) - with an average of ~4 molecular clouds along the line of sight. These multiple emission features make it difficult to assign a kinematic velocity to many of our sample. We have used archival CS (J=2-1) and maser velocities to resolved the component multiplicity towards 82 sources and have derived a criterion which is used to identify the most likely component for a further 202 multiple component sources. Combined with the single component detections we have obtained unambiguous kinematic velocities towards 580 sources (~80% of the detections). The 171 sources for which we have not been able to determine the kinematic velocity will require additional line data. Using the rotation curve of Brand and Blitz (1993) and their radial velocities we calculate kinematic distances for all components detected.
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