Team Melli beat Argentina 3-1 (25-19, 20-25, 25-22, 34-32) in Pool 7 at the Musashino Forest Sport Plaza in Tokyo.
Amir Ghafour finished top scorer with 26 points and Bruno Lima scored 18 points for Argentina.
Iran, who defeated Italy, China and Germany in Week 1, started the second week with a 3-2 loss to Brazil.
Iran is scheduled to meet Japan on Sunday.
The 2019 FIVB Volleyball Men's Nations League is the second edition of the FIVB Volleyball Men's Nations League, an annual international men's volleyball tournament contested by 16 national teams.
The competition is held between May and July 2019 and the final round will take place in the Credit Union 1 Arena, Chicago, United States.
This is the first edition of the World League or the Nations League to have the Final Round hosted in North America.