A method for operating a user equipment (UE) includes detecting that a beam failure has occurred, and based thereon, transmitting a first beam failure recovery request (BFRR) message at a first transmit power level on a first channel resource in a channel with a transmit power control mechanism configured to set the first transmit power level different from a first non-BFRR transmit power level of a first non-BFRR message transmitted on the first channel resource in the channel.