Advani remains a member of the BJP.
The resignation stunned the BJP. Most leaders -- until Monday morning buoyed by Modi's elevation -- declined to react initially, but later flocked to Advani's residence to persuade him to withdraw his resignation.
The Rashtriya Swayamsewak Sangh (RSS), the BJP's ideological parent, called it a "very unfortunate" development.
Within an hour, however, the BJP said it would try to persuade Advani to change his mind. Rajnath Singh tweeted that he had not accepted Advani's resignation.
BJP president Rajnath Singh Monday refused to accept party leader L.K. Advani's resignation from organisational posts.
"I have not accepted Shri Advaniji's resignation," Rajnath Singh said in a tweet.
BJP sources said that the party leadership would make efforts to persuade Advani to reconsider his decision.
Sharad Yadav of the Janata Dal-United, a BJP ally in the National Democratic Alliance, said: "It is sad...It is not good for NDA's health."
Yadav pointed out that it was Vajpayee and Advani, because of which his party had joined the NDA. Now his party would do a rethink, said Yadav.