Interesting paragraphs explaining the Boeing philosophy from the FCT 737 (TM) page 2.42 under the sub paragraph entitled Rejected Takeoff Maneuver
....The pilot not flying should closely monitor essential instruments throughout the takeoff roll and immediately announce abnormalities, such as "Engine Fire," Engine Failure," or any adverse condition significantly affecting safety of flight. The decision to reject the take off is the responsibility of the captain, and must be made prior to V1 speed.
If the decision is made to reject, the Captain must, without delay ;
Rapidly and simultaneously retard the thrust levers to idle and apply maximum braking, or verify proper operation of RTO autobrakes.
Immediately extend the speedbrakes and initiate reverse thrust consistent with the conditions.
Maintain maximum braking and reverse thrust as required, transitioning to the normal landing roll procedure after determining that stopping on the remaining runway is assured.
During the rejected takeoff, the First Officer calls "60 knots" during deceleration.
There are additional notes on the rejected takeoff manoeuvre, but the main points are that it is the captain who decides on the abort (not the first officer calling STOP). And it is the captain who handles every part of the physical process throughout the reject manoeuvre.