In simple terms the fuel consumption is proportional to the drag and drag is proportional to air density and speed squared.
Air density reduces roughly 3% for every 1000' increase in altitude so increasing altitude, in principle, allows you to go faster for the same fuel burn or use less fuel for the same speed.
This only holds true though to a limited degree as the drag increases disproportionately at low airspeeds due to the high angle of attack and at high airspeeds due to compressibility effects as you get to higher Mach numbers.
For small piston engined aircraft, the maximum range varies little with altitude, but the speed used to achieve max range increases with altitude. For atechnical explanation of that have a look at
this paper.
As you get higher the usable range between low indicated airspeed and high Mach number gets smaller for jet aircraft.