s of this page http://wiki.openstreetmap.org/wiki/Tag:boundary%3Dadministrative the administrative levels in Slovakia are:

admin level 6: Borders of Bratislava and Košice

admin level 8: district borders (because of this you see okres.... you see only district capital cities)

admin level 9: town, village or autonomous town in Bratislava or Košice.

So you should probably use something like that for Slovakia:

mkgmap:country=SVK & mkgmap:city!=* & mkgmap:admin_level6=* { set mkgmap:city='${mkgmap:admin_level6}' }
mkgmap:country=SVK & mkgmap:city!=* & mkgmap:admin_level9=* { set mkgmap:city='${mkgmap:admin_level9}' }

If you prefer to see autonomous parts of Bratislava and Košice,
ignore also admin_level 6.
You should completely ignore admin levels 7 and 8 to ignore district
borders and district names. I will test and let you know whether I

was succesful. I was also struggling with it and today I found the URL above.

Marek