Take the appropriate action and verify that the warning light turns off.

Taking Action
Message Indicated on DisplayMazda 6 Owners Manual: Fuel Gauge (Without Multiinformation Display)
The fuel gauge shows approximately how much fuel is remaining in the tank when
the ignition is switched ON. We recommend keeping the tank over 1/4 full.
If the low fuel warning light illuminates or the fuel level is very low, refuel
as soon as possible.
Refer to Warning Lights.
NOTE
...
Mazda 6 Owners Manual: Transmitter battery inspection
Caution
Since the battery voltage does not drop fully if the button is
pushed for only 4 seconds or less, it can not be properly examined to see
whether it is good or bad. Always push the button for 5 seconds.
Note
A correct measurement can not be obtained if the battery
temperat ...