What sort of thread is it? Is it 60 degrees, or more like trapezoidal with a flat top?
For folks with imperial lead screw lathes 4 TPI is relatively easy, my mini-lathe can cut it with "0" error. But I cannot cut 6mm pitch. Closest I can do is 6.032 mm pitch (0.54% error). You really need to measure the threads a little better. Can you cut 10 or more threads with the die and measure the total distance accurately? (Report the number of threads and the distance from crest to crest.) You will need a good quality scale or verniers. If the pitch is metric, all of the threads will line up very well on your (metric) scale.
If you can't do that, then I'd recommend finding a local machinist and ask them to measure the thread pitch accurately for you. Once you know the thread pitch, you can get a tap made. As others have mentioned, since you plan to cut wood with it, it does not have to be made out of high speed steel, nor hardened. Hardening wouldn't hurt, but could improve the tool life.