The pair were on a carriage with four children travelling between Edinburgh Waverley and Glasgow Queen Street stations when the incident happened.
Another passenger then began to use racist language to abuse the women verbally. The women then moved to a different part of the train.
The incident happened at around 7.25pm on August 2 and officers would now like to speak with the victims.
Anyone with information which could help to identify the victims has been urged to call British Transport Police on 0800 40 50 40, or text 61016, quoting reference number 1700053106.