In a speech broadcast live on state television, Rouhani said his government would overcome the economic challenges and show "the anti-Iranian officials in the White House" that the sanctions would fail.
"The economic problems are critical, but more important than that is that many people have lost their faith in the future of the Islamic Republic and are in doubt about its power," said Rouhani, who was attending a parliamentary session to answer lawmakers' questions about his handling of the economy, amid rising prices and unemployment.
"We are not afraid of America or the economic problems," he said. "We will overcome the troubles."
It was the first time the parliament summoned Rouhani, who is under pressure from hardline rivals to change his cabinet after a deterioration in relations with the United States and Iran's growing economic difficulties.
Lawmakers questioned Rouhani on topics including the rial's decline, which has lost more than half its value since April, weak economic growth and rising unemployment.