Advani chose not to go to the meeting in the party office on a day of hectic activities triggered by the demand for Gadkari's resignation by party MP Ram Jethmalani in the wake of allegations of dubious funding for his company Purti.
Just before the Core Group meeting, senior leaders Sushma Swaraj, Ananth Kumar and Balbir Punj met Advani, apparently to persuade him not to push for Gadkari's exit.
Earlier, Swaraj tweeted to "reiterate" her support to Gadkari and deny media reports that she was not supporting him.
The Core Group meeting topped a series of consultations among senior leaders, with Gadkari driving to the residences of Swaraj and Arun Jaitley to discuss the situation.
A day after his son Mahesh quit the BJP National Executive protesting against Gadkari's continuance, Jethmalani raised the pitch for the resignation of the party chief and claimed that some other senior leaders like Jaswant Singh, Yashwant Sinha and Shatrughan Sinha were with him on the issue.
RSS ideologue S Gurumurthy appeared to take the role of a mediator as he met Advani and later Jethmalani in a bid to persuade him to relent on the issue.
Jethmalani said he would like to check the documents on the basis of which Gadkari is claiming innocence.
Meanwhile, two senior party leaders Mukhtar Abbas Naqvi and Vinay Katiyar held a separate meeting and are understood to have shared the view that BJP's image had suffered because of allegations against Gadkari and something needed to be done immediately.
