Both "on" and "about" can be used.
If you comment on a situation, or make a comment about it, you give your opinion on it.
e.g. Mr Cook has not commented on these reports.
e.g. I was wondering whether you had any comments.
If you remark on something, or make a remark about it, you say what you think or what you have noticed, often in a casual way.
e.g. Visitors remark on how well the children look.
e.g. Martin made a rude remark about her t-shirt.