The Austrian newspaper Kurier reported on Friday that the exercise at Spielfeld, which is expected to involve hundreds of police officers and troops, had been moved to 26 from 25 June.
The Austrian Interior Ministry confirmed postponing the exercise by a day for the Austrian press agency APA, citing Slovenian Statehood Day as the reason.
However, the Austrian government will go ahead with the exercise, which aims to test whether a new border protection unit called Puma is capable of managing a potential new inflow of migrants.
Slovenian Interior Minister Vesna Györkös Žnidar protested against the exercise in a letter to her Austrian counterpart Herbert Kickl on Wednesday.
She raised her objection because part of the exercise is to take place on the Slovenian territory and because this "suggestion of the mass arrival of illegal migrants from the Slovenian to the Austrian side would inevitably have a very negative effect in Slovenia and likely in Austria".
The minister argued that the exercise "will contribute in no way whatsoever to the good relationship between our countries or our joint efforts to control the migration situation in the region".
She expressed the belief that Austria was exaggerating, underscoring that Slovenia was efficiently protesting the external Schengen border and working hard to prevent a repeat of the migration wave seen in 2015 and 2016.
As proof she noted that Austrian law enforcement authorities returned only 13 migrants to Slovenia so far this year and 39 throughout last year.