The agents, one of whom was Peter Strzok, didn’t warn Mr. Flynn that lying to them was a crime. Mr. Strzok was later dismissed from the FBI after sending political text messages that critics said showed bias against Mr. Trump and his associates.

The FBI “decided the agents would not warn Flynn that it was a crime to lie during an FBI interview because they wanted Flynn to be relaxed, and they were concerned that giving the warnings might adversely affect the rapport,” according to an internal FBI memo quoted by Mr. Flynn’s attorneys in the sentencing memo.

Though no warning is necessary to bring a prosecution for false statements, the FBI often cautions witnesses that lying is a prosecutable offense.