A network interface for a connection-based communication network has support for remote operations with reply, such as a remote read operation, that bypass host computer interaction. Such a network interface has support for general message processing operations which bypass host processor involvement. Message processing is low level processing of message between the host computer and the network. Such processing is performed on transmission in response to control information provided by the host and is performed on reception in response to control information included in incoming messages. Message processing includes low latency remote read and remote write operations, message filtering, and message demultiplexing. Such a network interface handles incoming messages containing destination control information indicating an operation to be performed, and possibly one or more operands. The network interface processes destination control information from a received message using a message coprocessor or equivalent operational logic. For such a network interface to support message processing, it includes mechanisms for extracting destination control information from a message and for inserting destination control information into a message. The network interface maintains information for each connection that indicates where the destination control information is located in any message received or transmitted over the connection. By providing for a queue of transmit requests between the receive and transmit sides on the network interface, support is provided for remote read operations or other operations invoking a reply which bypass the host processor. The queue can be appended by the receive side in response to a message processing operation performed on a received message. The queue is read by the transmit side to generate an outgoing message as if the queue provided transmit requests like the host computer.