Ajmer Congress committee president Vijay Jain said the posts had appeared on the social media accounts of the district's Congress Committee general secretary Naurat Gurjar and Youth Congress secretary Sarvesh Pareek yesterday, and was later removed.
"The posts had controversial remarks about Rahul Gandhi and his family and I have informed the Pradesh Congress Committee office about this. Action against them has to be taken by the party's state leadership," Mr Jain said.
When contacted, Naurat Gurjar said that someone else posted the derogatory remarks on his Facebook account.
"Someone uploaded the post on my Facebook account and as soon as I came to know about it, I removed the post yesterday only," he said on Wednesday.
Youth Congress and NSUI members today held protests and demanded action against Mr Gurjar and Mr Pareek.
"Both of them uploaded the posts yesterday against Rahul Gandhi which created resentment among the youths associated with the party. They should be expelled from the party for such act," youth Congress leader Yasir Chisti said.