Rekik and the 21-year-old Bruma, signed from Chelsea two months ago, are part of a youthful PSV side who have drawn much praise for their showings in the early stages of the new Dutch league and in Tuesday's 1-1 draw with the Italians.
But the 22-man squad for away matches against Estonia in Tallinn on September 6 and Andorra four days later, announced by the Dutch football association on Wednesday, is again without Wesley Sneijder, surprisingly dropped for friendly against Portugal last week.
Van Gaal said at the time Sneijder was not fit enough. Jonathan de Guzman, fellow midfielder Kevin Strootman and striker Klaas Jan Huntelaar all miss out with injuries.
The Netherlands are seven points clear in Group D and will qualify for Brazil if they win their next two games.
Squad
Goalkeepers: Kenneth Vermeer (Ajax Amsterdam), Michel Vorm (Swansea City)
Defenders: Daley Blind (Ajax), Jeffrey Bruma (PSV Eindhoven), Stefan de Vrij, Bruno Martins Indi, Joris Mathijsen (all Feyenoord), Karim Rekik (PSV Eindhoven), Ricardo van Rhijn (Ajax Amsterdam), Paul Verhaegh (FC Augsburg), Ron Vlaar (Aston Villa)
Midfielders: Jordy Clasie (Feyenoord), Stijn Schaars (PSV Eindhoven), Rafael van der Vaart (Hamburg SV), Marco van Ginkel (Chelsea), Georginio Wijnaldum (PSV)
Forwards: Dirk Kuyt (Fenerbahce), Jeremain Lens (Dynamo Kiev), Arjen Robben (Bayern Munich), Ruben Schaken (Feyenoord), Robin van Persie (Manchester United), Ricky van Wolfswinkel (Norwich City).
(Reporting by Mark Gleeson in Cape Town, editing by Pritha Sarkar)
