Senior QED leader Athar Zamal Lari said the letter had been sent to the "secular" parties on Saturday with the aim to defeat "communal" BJP in the temple town of Varanasi.
Quami Ekta Dal has other smaller political outfits in its fold such as Bharatiya Samaj Party, Rashtriya Parivartan Dal, Janvadi Party and Phullan Sena.
SP has already rejected the proposal to field a joint candidate with QED, saying "we will not take support from any 'goonda, badmaash' (hooligan)...."