This is what the FAA's AIM says about it:
5−5−15. Minimum Fuel Advisory
a. pilot.
1. Advise ATC of your minimum fuel status hen your fuel supply has reached a state where, upon reaching destination, you cannot accept any undue delay.
2. Be aware this is not an emergency situation, but merely an advisory that indicates an emergency situation is possible should any undue delay occur.
3. On initial contact the term “minimum fuel” should be used after stating call sign.
4. Be aware a minimum fuel advisory does not imply a need for traffic priority.
5. If the remaining usable fuel supply suggests the need for traffic priority to ensure a safe landing, you should declare an emergency due to low fuel and report fuel remaining in minutes.
b. Controller.
1. When an aircraft declares a state of minimum fuel, relay this information to the facility to whom control jurisdiction is transferred.
2. Be alert for any occurrence which might delay the aircraft.