Mukherjee had yesterday in Nagpur warned that any attempt to define India through "religion, hatred, dogmas and intolerance would dilute our existence" and said public discourses must be freed of all forms of violence.
Former Finance minister P Chidambaram said Mukherjee had told the RSS what was correct about the Congress's ideology.
"Happy that Mr Pranab Mukherjee told the RSS what is right about Congress' ideology. It was his way of saying what is wrong about RSS' ideology," he said on Twitter.
Congress spokesperson Abhishek Singhvi said one should not judge a man by the invitation he gets, but by what he speaks. Mukherjee's address vindicates this, he said.
"Very happy that my stand from day one fully vindicated viz don't judge a man by the invitation or the host's identity but by what he says and does at the event. repeated this and Pranabda's address fully vindicates this view. He is first ex Congman to preach some lessons to RSS," Singhvi said on Twitter.
"Having invited Pranabda, would be great if RSS tried to imbibe fractionally his home truths and plain spoken verities. Learn from those whom you invite as educators and mentors!" he tweeted.
Senior Congress leader Anand Sharma said he hoped that the RSS would absorb the former president's message.
"Pranam Pranab da, you have emerged proud and taller from Nagpur. There was never any doubt about your strength of character, moral courage, conviction and commitment to uphold the secular constitutional democracy," he tweeted.
"You told the RSS about the richness and diversity of India's pluralism. Hope they will reflect and absorb your message," Sharma said.
He had criticised Mukherjee yesterday, claiming that the images of the former president at the RSS headquarters had anguished those who believe in pluralism and diversity of India.
"The images of Pranab Da, veteran leader and ideologue at RSS Headquarters have anguished millions of Congress workers and all those who believed in pluralism, diversity and the foundational values of the Indian Republic," Sharma had said soon after images of Mukherjee from Nagpur appeared on TV.
The Congress leader's tweet came in response to the Sangh stating, following the controversy over Mukherjee's visit, that dialogue was important, central to RSS ideology and an old tradition of the country.
The Congress, after a lot of unease within the party over the former president's visit to Nagpur, had said Mukherjee has showed the mirror of truth to the RSS.
It had also asked the Sangh and the BJP whether they would admit their mistakes and change their "character, orientation, thought process" after accepting his "sagacious advice".
Congress communications in-charge Randeep Surjewala said Mukherjee, in his speech, had reminded the RSS of India's pluralism, tolerance, secularism and inclusiveness.
He hoped that the RSS would come out with a reply admitting its mistakes and doing course-correction.