Bansal was a special invitee today to the meeting of the Congress Core Group, hours after party general secretary Janardhan Dwivedi dismissed the Opposition's demand for the Railway Minister's resignation.
The minister had earlier met the Prime Minister.
Besides Gandhi and Singh, senior leaders Ahmad Patel, A K Antony, Sushilkumar Shinde and P Chidambaram are members of the Congress Core Group.
Bansal's nephew V Singla was yesterday arrested by CBI, which also held a Member of the Railway Board in connection with alleged bribery of Rs 90 lakh for fixing a top-level position in the government.
Earlier in the day, Congress brushed aside Opposition demands for Bansal's resignation, saying it has become a "disease" of the Opposition to make such demands.
"For those who are demanding resignation, it has become a disease," Congress General Secretary and head of media department, Janardan Dwivedi told reporters.