A two-hour long meeting Tuesday between Rane, Chavan and state Congress President Manikrao Thakre, failed to resolve the crisis which has attracted criticism from within the party and outside.
"I have insisted that my resignation should be accepted. Chavan tried to persuade me to withdraw it. I have told him that the issues I have raised in the letter must be addressed first," Rane told media persons after the meeting.
Referring to speculation that he may be given the post of state Congress chief, Rane said that no fresh proposals have been made by the party so the best solution would be to accept his resignation. He stressed he would continue to remain in the party.
"It has now been decided that within the next two days, Chavan will seek an appointment on this issue with Congress president Sonia Gandhi. Chavan, Thakre and I shall go to meet her and discuss the issue," he said.
On his part, Chavan informed the media that he had requested Rane to withdraw the resignation and also assured him that the issues raised by him would be conveyed to the party's central leadership.
"I am hopeful that this matter will be sorted out through negotiations," he said.
Chavan also said that Thakre and Rane discussed other party issues, organizational and administrative matters and the strategies for the forthcoming assembly elections.
"I will brief the party high command and general secretary Mohan Prakash (who is in-charge of Maharashtra) on these discussions. I will try to solve the state-level matters raised by Rane," he said.
With assembly elections barely three months away, Rane quit as industry minister Monday - the second time in two months - sending shock waves through the Congress.
He also attacked party leaders for not honouring their commitment of making him chief minister within six months of his joining the party in 2005, noting he has waited for nine years now.
Rane criticized Chavan for slow decision-making, lack of control over the administration and other issues which affected the Congress showing in the last Lok Sabha elections.
He also expressed grave doubts over the party showing in the upcoming assembly elections in such a scenario and said he did not want to be a partner in defeat.
Rane, who was the chief minister for nearly a year at the fag end of the Shiv Sena-BJP regime of 1995-1999, had quit the Shiv Sena to join Congress in 2005.