"The man is an RSS man. That is a known fact. We are curious to know if Indian embassy facilitated this meeting," Congress leader Rahul Gandhi told reporters. His party men also raised Mr Vaidik's remarks to a Pakistani channel that there is no harm in freedom for Kashmir.
"Such views had never been openly expressed even by Kashmir separatists," Congress leader Ghulam Nabi Azad in the Rajya Sabha, calling it a question of national security.
Mr Vaidik had told Pakistan's Dawn TV that a solution on Kashmir has to be acceptable to the people of Kashmir before India or Pakistan.
"No Pakistani leader has said that free Kashmir is acceptable to them," he said. Asked whether India would accept it if Pakistan did, Mr Vaidik said, "If Kashmiris on both sides agree and if both countries agree then there is no harm in it."
Finance Minister Arun Jaitley remarked that it was the "diplomatic misadventure of a private individual."
But Congress members insisted on action against the journalist. Slogans demanding his arrest were also raised.
Speaking for the first time on the row, Foreign Minister Sushma Swaraj said in the Lok Sabha, "This was his private travel and a personal meeting. The allegation that Indian government facilitated it is false and extremely unfortunate. The government has nothing to do with this."
Mr Vaidik, 69, met Hafiz Saeed on July 2 while touring Pakistan along with a group of journalists and politicians invited by a peace research institute. He is considered close to yoga teacher Ramdev, who campaigned for the BJP in the national election.
Mr Vaidik said he met Hafiz Saeed as a "journalist must meet all kinds of people."
New Delhi accuses Saeed, founder of the Pakistan-based terror outfit Lashkar-e-Taiba, of plotting a series of terror strikes in India, including the 26/11 Mumbai attacks in 2008, in which 166 people were killed. Saeed, however, roams free in Pakistan and often addresses public rallies.