Agarwal, who is a Supreme Court lawyer, said he received the handwritten threat letter yesterday afternoon, following which the complaint was filed at the Hazrat Nijamuddin police station.
"The letter written in Hindi used filthy and abusive language against me and BJP national leaders. The letter writer also threatened to kill me," he said.
Agarwal had polled 1,73,721 votes in the 2014 Lok Sabha election. He was defeated by Sonia Gandhi by a margin of about 3.52 lakh votes.
Police said a case of criminal intimidation has been registered and investigation launched.