Togadia, who was quoted by the media as saying that Muslims should be thrown out of Hindu areas, has termed the news report "fabricated" and slapped a legal notice against the media.
The Aam Aadmi Party (AAP) strongly condemned the speech by the Vishwa Hindu Parishad (VHP) chief in Bhavnagar, Gujarat, Saturday when he targeted Muslims for buying properties in certain areas.
The AAP described the speech as "extremely shocking and a shameful act" and added that it "goes against the constitution which provides equality and freedom for every citizen".
The AAP demanded that the Election Commission "should direct immediate registration of an FIR against Togadia and should take strict action against him, so that he is not allowed to vitiate the peaceful atmosphere during elections".
Bharatiya Janata Party (BJP) spokesperson Prakash Javadekar defended Togadia, saying: "I talked to Togadiaji. He said he did not make such a statement."
Rashtriya Swayamsevak Sangh (RSS) leader Ram Madhav echoed similar sentiments.
"Pravinbhai had not said anything that was attributed to him. It was a fabricated news. No Swayamsevak thinks on those lines," Madhav tweeted.
"No RSS member would ever force such views... We are one nation," he said.
Togadia in his legal notice described the media reports as "false, malafide and mischievous".
He also said the media reports, including by the electronic media, show that "there is a bigger conspiracy" against him to defame him and put his life and those of his kin and his aides in danger.
Togadia's alleged hate speech made in Bhavnagar comes close on the heels of BJP candidate from Bihar's Navada constituency, Giriraj Singh, saying that those who oppose the party's prime ministerial candidate Narendra Modi should be sent to Pakistan. Singh has justified his statement.
Amit Shah, the BJP general secretary in-charge of party affairs in Uttar Pradesh, was also pulled up by the poll panel for his hate speech in Muzaffarnagar.
The Election Commission banned Shah from campaigning, but it allowed him to resume it after he apologised.
The AAP said Togadia's statement and those by Giriraj Singh and Shah show that "the BJP and its associated organisations like the VHP are trying to inflame communal feelings and communalise the situation in the country for votes".
Congress leader and union minister Kapil Sibal said Togadia's statement "spreads venom".