Use a resistor in series with the LED. Start with 100 ohm and see if that is bright enough. If not reduce the value of the resistor.
I have some super bright white LEDs that are easily visible at only 1 ma

Using a resistor does not solve the problem. It cannot adequately regulate current of a 3.0 to 3.4V LED with a 3.0V battery that will drop in voltage over its life.

The correct solution is to use 3AAA cells to power the LED and an LDO for the micro.

 

It solves the problem of not overloading the micro and why does it have to be regulated?

 

I have no doubt that the LED is adequately bright at a lower voltage. Illumination and current of LEDs is very non-linear, especially in areas not close to the published operation point. Besides that, human perception of brightness is also non-linear! And the output of an LED at 10 mA looks similar to the output at 20 mA in many instances. I used to drive those "high brightness" LEDs from Digikey directly from 5 volt CMOS gates and the brightness was very adequate. Was it close to RATED? No, nor did that matter.

AND!!! If the brightness is adequate how well does the current need to be regulated?? This is NOT "Mars probe rocket science."