Kyrgios made the statement on his Facebook page after Bernard Tomic suggested the 20-year-old might consider a boycott in sympathy with his friend and fellow player.
Tomic was dropped from the team for the July 17-19 tie at the weekend after launching a tirade at Tennis Australia officials in the wake of his third round defeat to champion Novak Djokovic at Wimbledon.
"As a proud Australian it's a pleasure and privilege to be able to represent my country in Davis Cup," Kyrgios posted.
"As long as I'm able, fit and healthy, It's an opportunity I will never pass up."
Kyrgios faces Frenchman Richard Gasquet in a last 16 tie at Wimbledon later on Monday.
Tomic has accused Tennis Australia of neglecting him and his sister Sara, whose funding was cut by the national body because of an uncooperative attitude of their controversial father and coach John.
(Reporting by Nick Mulvenney; Editing by John O'Brien)
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