I have seen this many times on 96 GTI's and it is usually caused by a gummed up throttle butterfly so seeing as this is cheaper than the routes suggested by golfvr6, I'd try it first;
To clean it, disconnect the air intake pipe at the throttle body and you should be able to see the butterfly.
Spray on some carb cleaner or other solvent and wipe off as much gunk as you can. It helps if you operate the throttle by hand at the same time so you can get to the back of it.
Put it all back together and off you go. You should now see the revs rise every so slightly as the clutch is depressed and the drop gradually to about 900rpm.
Let us know how you get on.