That works on a machine with enough power and a material that will allow it. What you might be looking for is called a box tool that were often used in automatic screw machines and turret lathes.
I think there is a drawing on Harald Halls site but not sure. Basically a box tool has a hole through it not much bigger than your stock and braces usually one opposite the cutting tool and one on top to resist cutting forces. Cutting tool is ground from HSS and comes in from normal direction.
Set up takes a bit of time but if you start with something the finish size and then adjust to final size it is not hard. Takes a few runs to dial in then cut until your tool goes blunt.
That tool would likely go down to the size you require, it's also known as a Roller Box, it's fairly easy to make one if you can't buy one, I have a couple and work in the 1mm to 4mm range with them.
Last week I made a batch of parts from 1/4" Titanium with a 50mm long section around 3mm, some setting up then one pass each for 50 parts ;-)
If you want to make the tool yourself google (Frank Ford follow rest ) he made a neat little tool that should do the job for you. He shows all the parts.
I have made a homemade box tool that cut .375 down to .125 dia times 4 inches long and it worked great. I ran a few hundred parts with it.