"The RSS is a nationalist organisation," the minister tweeted in Hindi.
"It should be made mandatory for all people of the country to spend some time with the sangh. Many problems of the country will be solved," he added.
The tweet, however, made no direct mention of Mr Mukherjee's decision to attend the Rashtriya Swayamsevak Sangh event.
Recently, he compared Rahul Gandhi to the deadly Nipah virus, saying whoever comes in contact with him will be destroyed.
He had once demanded that the cow should be declared a national animal.
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