The meeting was the second such consulations held by Gandhi during the day. Earlier, she had held a strategy session with some senior leaders.
The second part of the budget session is commencing from Monday and is scheduled to conclude on May 10.
The meeting of the core group, headed by Gandhi, took place at a time when a controversy has hotted up over the leakage of draft report of the JPC on the 2G spectrum allocation scam.
BJP has dubbed the draft JPC report as a "cover-up" attempt to "save" Congress leaders, including Prime Minister, and vowed to raise it in Parliament.
Also Read
Left parties have also strongly criticised the "deliberate leak" of the draft report, saying it amounted to breach of parliamentary privilege and sought a probe into it.
BJP has been pressing for setting up of a Special Investigation Team to probe alleged government interference in the coal scam report.