The BJP had earlier filed a complaint with the Election Commission against Mr Vishwas, claiming he made the comments at an election rally where AAP chief Arvind Kejriwal was reportedly present.
The BJP has said this is a violation of the model code of conduct and asked the Election Commission for action on their earlier complaints too. Ms Bedi has also filed a police complaint.
While the AAP has said the video clearly proves that Mr Vishwash never made any comments against Ms Bedi, the BJP has shot down the argument.
"Ms Bedi is our main campaigner. If this comment was not made against Ms Bedi, who was it made against," BJP MP Meenakshi Lekhi told NDTV.
But Mr Vishwas accused the BJP of levelling false charges against him as the party had no "Delhi-centric issues to fight these elections on, so they are resorting to such tactics".
"I challenge the BJP and Kiran Bedi to show the video where I made the comments. If charges against me are proved, I will resign from public life," he told NDTV.
Mr Vishwas claimed that he had never mentioned Ms Bedi "without respect". "I refer to her as Badi Behen (elder sister)," he said.
Both Ms Bedi and Me Kejriwal were members of activist Anna Hazare's nation-wide campaign against corruption in 2010. While Mr Kejriwal launched the AAP in 2012, Ms Bedi, a former IPS officer, joined the BJP on January 15 this year.
Mr Vishwas is a poet and stage artist who has been a prominent member of the AAP since the party was launched. He was handpicked by Mr Kejriwal to take on Congress vice-president Rahul Gandhi in the latter's family bastion Amethi.