"Those who make the allegations must provide the needed proof. What is your evidence?" Rouhani told reporters, a day after addressing the UN General Assembly.
The United States, France, Germany and Britain have all blamed Iran for the strikes on the kingdom's Abqaiq plant and the Khurais oil field which knocked out half of Saudi Arabia's oil production.
A series of drone and missile attacks on the oil facilities of Saudi Aramco, the country's largest petroleum company, occurred on September 14, severely impacting the global oil market and triggering fresh tension between Saudi Arabia and Iran.
However, Saudi Arabia has vowed to identity and take action against those behind the attacks.