The letter, written in a BNP letterhead, was sent on Saturday.
In the letter, Fakhrul said, "I urge the Facebook authorities to take necessary steps to rid me of the embarrassment of fabricated statements and opinions being circulated in my name through fake Facebook accounts."
He also said a vested quarter has long been circulating different false statements and opinions in his name by opening fake accounts.
The BNP leader also said he himself never opened any Facebook account in his name.
Later, in a statement, Fakhrul said he has long been observing that various statements, remarks and opinions are being posted on the Facebook by opening fake accounts in his name.
"I would like to clearly say I didn't open any Facebook account. So, I don't have any involvement in the opinions of the fake Facebook accounts and I won't be responsible for those either."
He urged those running the fake FB accounts in his name to refrain from doing such malpractice.