The accused had allegedly demanded extortion money of Rs 10 crore from Tulsipur MLA Mashud Khan.
"We have detained two persons in connection with threatening the MLA, whose security has been enhanced," Superintendent of Police VD Shukla said.
Tulsipur MLA Mashud Khan had received two threatening letters in a gift pack.
Khan had received two threatening letters in a gift pack after Diwali in which Rs 10 crore was demanded from him, he said.
Later, the legislator also got phone calls threatening him of dire consequences if he failed to pay the amount, the official added.