Meanwhile, party leader M Veerappa Moily had on Friday said there is not even one per cent possibility of Gandhi continuing as party president.
Congress' general secretary in charge of Madhya Pradesh Dipak Babaria and Goa unit chief Girish Chodankar, resigned on Friday, after MP Vivek Tankha quit as the chairman of the party's legal and human rights cell and urged others to follow suit to give a free hand to Rahul Gandhi to restructure the party at all levels.
Both Babaria and Chodankar took the responsibility for the Lok Sabha poll debacle of the party in their respective states.
Delhi PCC's working president Rajesh Lilothia and Telangana Pradesh Congress Committee working president Ponnam Prabhakar also quit, as also a number of other office-bearers in various states.
A common letter of resignation was being circulated on social media with the names and signatures of certain Congressmen, including those of Haryana Mahila Congress chief Sumitra Chauhan and All India Congress Committee (AICC) secretaries Rajesh Dharmani and Virender Rathore.
However, there was no official word from the party about the letter.
Madhya Pradesh Chief Minister Kamal Nath has said he had offered to resign as the state Congress chief after the party's debacle in the recently-concluded Lok Sabha polls.
His remarks come in the backdrop of reports that Gandhi has expressed disappointment that none of the party leaders, holding top posts, took the responsibility for the party's poll rout after he himself offered to resign last month.
Ever since his offer to resign at a Congress Working Committee (CWC) meeting, Gandhi has maintained that he will not go back on his decision as it was taken to ensure accountability for the party's poor poll show.
"I have offered to resign taking full responsibility and to ensure accountability for the party's defeat in the Lok Sabha election. I cannot ask others to resign. It is up to them if they want to take responsibility," he told Congress leaders from Haryana after they urged him to take back his decision.
At the AICC briefing, replying to a question, Congress spokesperson Manish Tewari said the CWC had asked Gandhi to continue as the party chief and rejected his resignation.
"The general opinion within the party is that Rahul Gandhi should continue as the Congress president and various leaders have expressed their views at different fora. But the basic issue is that he should remain on the post," he said.
Tankha resigned as the chairman of the party's legal and human rights cell on Thursday and urged others to follow suit.
"We all should submit our resignations from party positions and give Rahul-ji a free hand to choose his team. I welcome Mr Kamal Nath's statement to that effect. I unequivocally submit my resignation as AICC Dept chairman Law, RTI and HR. Party cannot afford a stalemate for too long," he wrote on Twitter.