Kurz made the comments in Vienna on Tuesday after Iran and the Group 5+1 (Russia, China, the US, Britain, France and Germany) reached a conclusion on a comprehensive nuclear agreement over Tehran's nuclear energy program.
"Today is a historic day, and we are glad this agreement was achieved. I congratulate the Iranian people on this deal. I will travel to Iran along with Austrian president in September," Kurz told the Tasnim News Agency.
Austria has been playing host to many rounds of nuclear talks between Iran and world powers, including the final and most decisive round that began more than two weeks ago.
On Tuesday, the negotiating parties reached a conclusion over the text of the agreement after about 23 months of negotiations.