Mr Gandhi launched the broadside against the BJP's ideological mentor as he wrapped up his four-day tour of Karnataka, where elections will be held this year.
"In every single ministry in India, at the national level there is an OSD (officer on special duty) from RSS working with the minister... The minister is not operating on his own," Mr Gandhi said, according to news agency PTI.
"The approach is of capture, the approach is here is an institution and let us capture it, as opposed to allowing an institution to serve the people of India and allowing the people of India to capture the institution," the Congress president said.
Addressing the businessmen, Mr Gandhi said the overnight ban of high-value currency notes in November 2016 was an idea given by a "particular ideologue" of the RSS to Prime Minister Narendra Modi. "Do you know where the idea of note-bandi (note ban) came from? It was not RBI (Reserve Bank of India), it was not (Finance Minister) Arun Jaitley, it was not an officer in the Finance Ministry," Mr Gandhi said.
"This is the fundamental conflict we have with BJP. Their idea is wherever they go they plant people with their ideology into that organisation," he said, adding the Congress's idea is to democratise institutions while BJP believes in bureaucratising them.
"It was a particular ideologue of the RSS. Now you imagine the RSS places an idea into the Prime Minister's mind and the Prime Minister launches that idea," Mr Gandhi said.
The Congress president has said his party would drastically reform the national tax GST - which he called Gabbar Singh Tax after the Bollywood villain -- if it came to power.
PM Modi, who campaigned for his party in Karnataka on February 4, had criticised the Congress over the deaths of some BJP volunteers. "With the Congress government in the state, what makes news is ease of doing murder," PM Modi had said.
Karnataka is the only state in south India where the BJP came to power once.
The party is going all-out to wrest power from the Congress in the assembly elections, with state BJP chief BS Yeddyurappa intensifying attacks on Chief Minister Siddaramaiah over allegations of corruption.
With inputs from PTI