"The US government over the last two years, violating all the international structures and rules and using its economic, financial and military resources, has taken an aggressive approach and presents a serious risk to stability in the region and the world," Rouhani said, in translated comments, at a meeting of the Shanghai Cooperation Organisation.
The two tankers, one Norwegian- and one Japanese-owned, were set ablaze in the Gulf of Oman off the coast of Iran on Thursday, escalating tensions across the region and sending world oil prices soaring.
US Secretary of State Mike Pompeo had said earlier that Iran was responsible for the attack that occurred in the Gulf of Oman.
"This assessment is based on intelligence, the weapons used, the level of expertise needed to execute the operation, recent similar Iranian attacks on shipping," Pompeo said.
US military tried to back up Pompeo's claim asserting that the Iranian Revolutionary Guard Corp Gashti Class patrol boat approached the Kokuka Courageous "and was observed and recorded removing (an) unexploded limpet mine from the M/T Kokuka Courageous."
The US also released a video of the incident.
The United Arab Emirates said Friday that twin attacks on tankers in the Sea of Oman just weeks after four ships were damaged off the UAE coast marked a dangerous escalation".
"The attack against the tankers in the Gulf of Oman is a worrying development and a dangerous escalation," the UAE minister of state for foreign affairs, Anwar Gargash, said.
Iranian Foreign Minister Mohammad Javad Zarif charged that the US administration had "immediately jumped to make allegations against Iran without a shred of factual or circumstantial evidence".
He accused it of seeking to "sabotage diplomacy" as Japanese Prime Minister Shinzo Abe visited Tehran in a bid to ease Iran-US tensions.
(With inputs from agencies)
'The US government over the last two years, violating all the international structures and rules and using its economic, financial and military resources, has taken an aggressive approach and presents a serious risk to stability in the region and the world,' Rouhani said.