Well, there's yer problem, Berg header pins are only 0.025in (0.64mm). :)
Browsing Digikey, you can select the 'Pin Size - Above Flange' to be what you want for a snug fit. I don't see any exactly 1.00mm, but 1.02 or 1.04mm is pretty close.
For example, This might work or This if you want gold...