Gandhi has been repeatedly saying that Modi's name has figured in the documents listing those who have been paid alleged bribes by the corporate giants.
The documents were seized by the Income Tax Department in raids on Sahara and Birla offices in 2014. The documents have names of other politicians, including Congress' Uttar Pradesh chief ministerial candidate Sheila Dikshit.
"The Prime Minister is telling the nation that he is fighting against corruption but when it comes to allegations against him, he does not respond," Gandhi said at a press conference, also attended by other opposition parties like the Trinamool Congress, the Rashtriya Janata Dal, the DMK and Jharkhand Mukti Morcha.
The Congress leader said while Modi was responding on all other issues, he was silent on questions raised on his "honesty and integrity".
Gandhi asked that when former Delhi Chief Minister Dikshit was open to an investigation, "why is the Prime Minister shying away from a probe".
He said four of Congress ministers resigned when their names surfaced in Jain Hawala Diaries case.
"The Prime Minister should be the first person to say if I am facing allegations, then there should be an inquiry," Gandhi said.