Methods, systems, and devices for wireless communications are described. A user equipment (UE) may generate an uplink random access message, including a random access preamble and an uplink shared channel resource unit, of a two-step random access procedure. The UE may identify configuration information for uplink control information (UCI) multiplexing. The UE may identify a trigger for inclusion of UCI with the uplink random access message. The UE may multiplex the UCI and a reference signal with the uplink shared channel resource unit and map the uplink control information to resource elements in the uplink shared channel resource unit based on a priority of the uplink control information and a location of resource elements to which the reference signal is mapped. The UE may transmit the uplink random access message comprising the uplink control information and an indication of the used UCI configuration to the base station.