Washington is to start reimposing economic penalties on Tehran in coming months after US President Donald Trump quit an agreement between major world powers and Iran in which sanctions were lifted in return for curbs on its nuclear program.
This may cut Iran's hard currency earnings from oil exports, and the prospect is triggering a panicked flight of Iranians' savings from the rial into dollars.
On Monday, police patrolled Tehran's Grand Bazaar as security forces struggled to restore normality after clashes with protesters angered by the rial's collapse, which is disrupting business by driving up the cost of imports.
Defending his economic record, Rouhani said the government's income had not been affected in recent months, and the fall in the rial was the result of "foreign media propaganda".
"Even in the worst case, I promise that the basic needs of Iranians will be provided. We have enough sugar, wheat, and cooking oil. We have enough foreign currency to inject into the market," Rouhani said in a speech broadcast live on state television.
Rouhani said the fresh US sanctions were part of a "psychological, economic and political war", adding that Washington would pay a high price for its actions.
"Withdrawal was the worst decision he (Trump) could make. It was appalling. It hurt America's global reputation," he said.
Protesters angered by Iran's cratering economy confronted police in front of parliament on Monday, with security forces firing tear gas at them, according to online videos, the first such confrontation after similar demonstrations rocked the country at the start of the year.
The unplanned demonstration came a day after protests forced two major shopping centers for mobile phones and electronics to close in Tehran and after demonstrators earlier closed its Grand Bazaar.