The controversy erupted after a photo of the letter found its way to the social media.
"BJP people are so afraid of losing Varanasi that they are spreading fake pics of AAP thanking M Ansari for support," AAP posted on its official Twitter account in reaction to the letter being circulated.
Warning of "legal action" for defamation, the party said that the 'fake' letter was written on a different letter-head than its original one.
Qaumi Ekta Dal's Ansari, currently in Agra jail, is an MLA from neighbouring Mau area. He had fought last Lok Sabha elections as a BSP candidate and had lost to BJP's Murli Manohar Joshi by a small margin at that time.
Ansari had earlier said he would contest Lok Sabha elections again this time, but later withdrew his plans.
His party said that Ansari has decided not to contest elections so that the secular votes do not get divided and that they would support the strongest candidate against BJP prime ministerial candidate Narendra Modi.
Since then, speculations had going around that Ansari was supporting Kejriwal. AAP, however, later clarified that it would not take support of Ansari, who has a rogue image in this area and is facing many criminal cases.
Meanwhile, Kejriwal has been continuing with his 'chaupals' in rural areas of Varanasi, which the party appears to have identified as key areas with minimal support for BJP and Modi.