The offshore field, which Iran calls South Pars and Qatar calls North Field, is shared between Iran and Qatar.
Iran's daily gas production from the field now exceeds that of Qatar, Zanganeh said.
France's Total and China National Petroleum Corp (CNPC) suspended investment in the South Pars project last year after the United States threatened to impose sanctions on companies that do business in Iran.
The United States reimposed sanctions on Iran's energy and banking sectors after Washington withdrew from the 2015 nuclear agreement between Tehran and world powers.
The agreement had imposed limits on Iran's nuclear ambitions in exchange for sanctions relief.