The meeting of the group, which also includes former party chief Nitin Gadkari and Arun Jaitley, took place today at Ahmedabad.
Party sources said that henceforth the core group would be taking key decisions.
Earlier, these decisions were taken by the party's Parliamentary Board, the highest decision-making forum which also has party veterans L K Advani and Murli Manohar Joshi, besides Sushma Swaraj, M Venkaiah Naidu, Ananth Kumar, Thawarchand Gehlot and Ramlal as its members.
All four members of the core group are already members of the Board.
Sources also suggest major changes in the party with Gadkari likely to be brought back as party chief and Rajnath drafted for a key ministry in the government.
The core group met today in Ahmedabad to decide on whether party veterans like Advani and Joshi will have a role in the government.
"As far as the roles of veteran leaders are concerned, I will call a party meeting to which they will be invited. After thorough discussions with all big leaders, we will decide what role will be played by which person," Singh told reporters at Ahmedabad airport on way to Gandhinagar to meet Modi.