Rouhani, a cleric and former nuclear negotiator, cleared the simple majority needed to secure victory in June 14 presidential elections in Iran. He was considered a moderate in comparison to the five other candidates.
The Iranian currency, the rial, collapsed under pressure from Western economic sanctions last year. U.S. and European sanctions are meant to starve Iran of the revenue needed to finance a controversial nuclear research program, which it maintains is for peaceful purposes.
Iran's state-funded broadcaster Press TV reported the value of the rial has rallied since Rouhani's victory. The national currency was valued at 30,000 per U.S. dollar, up 16 percent from the previous week, the report said.
Press TV reports Iranians holding U.S. currency are selling it in favor of the rial as the value rebounds. The broadcaster quotes an unnamed "currency dealer" as saying the rial should gain strength if Rouhani "strengthens ties with the West and some of the sanctions are removed."
Financial services provider Oanda Corp. paints a different picture. It reports a sharp drop-off in the value of the rial as of trading Monday.
Rouhani said he would rule as a moderate once he takes the oath of office in August. Iran's Supreme Leader Ali Khamanei has the ultimate say over Iranian policy decisions.