Protests over the Iranian government’s handling of the economy spread to several cities on Friday, including Tehran, in what appeared to be a sign of unrest.

President Hassan Rouhani began his second term in August after winning re-election on promises to revitalize an economy hurt by sanctions. Although foreign investment is rising, the country continues to survive mainly on oil sales. Youth unemployment stands at more than 40 percent, sluggish state-owned enterprises control significant sectors of the economy, and American sanctions prevent most international banks from providing financing or credit to Iran.

Many of the international sanctions against Iran were lifted under the 2015 accord on Iran’s nuclear program. But unilateral American sanctions on doing financial transactions with Iran remain in place, and the cumulative effect of sanctions has been severe. Mr. Rouhani, who heralded the agreement as a fresh start, has faced criticism for not doing enough to jump-start the economy.

The Trump administration seized on reports of the protests to denounce Iran. “Iran’s leaders have turned a wealthy country with a rich history and culture into an economically depleted rogue state whose chief exports are violence, bloodshed and chaos,” the State Department spokeswoman, Heather Nauert, said in a statement. “As President Trump has said, the longest-suffering victims of Iran’s leaders are Iran’s own people.” She added that the United States “strongly condemns the arrest of peaceful protesters.”