The unofficial rate in central Tehran was around 20,500 rials for the greenback, the official IRNA news agency reported.
The rate showed a 12-percent rise for the US currency since last Wednesday when it was changing hands at 18,000 rials on the black-market.
The Tehran government has tried to shore up the rial by imposing a lower rate in banks and currency exchange bureaus, while also banning transactions outside of such outlets, leading to the black-market operations.
Last week, Iran's central bank banned the possession of and transactions in foreign currencies, including the dollar, without an official invoice, warning that offenders would be prosecuted.
The bank has introduced a dual rate of 11,300 rials for state business and imports, and 14,000 for Iranian travelers.
But many exchange bureaus have refused to buy or sell dollars at the imposed rates, prompting the operation of a black-market despite police efforts to enforce the ban.
In late October, it cost about 12,500 rials to buy a dollar in Tehran.
A rush for gold and other non-currency assets has since taken hold, with the price of gold coins in Iran rising by 25 percent since January 18.
The currency crisis comes at a time when the United States and European countries are ratcheting up punitive measures against Iran to curb its controversial nuclear program.
Although the Iranian government has insisted there is no connection between the rial's slide and new sanctions, some officials have admitted a "psychological" impact as international sanctions spook ordinary Iranians.
Economy Minister Shamseddin Hosseini and central bank Chief Mahmoud Bahmani have vowed before the Iranian parliament to bring the exchange rate under control.
A sudden acceleration in the slide was seen after US President Barack Obama at the end of December signed into law more sanctions hitting Iran's central bank and targeting foreign firms which do business with the Islamic republic.
On Monday, the European Union agreed to slap an embargo on Iran's oil exports as the West ramped up pressure on Tehran's nuclear drive and urged it to return to the negotiating table.
A compromise agreement, due to be formally announced later the same day, provides for an immediate ban on importing Iranian crude and a gradual phase-out of existing contracts between now and July 1, diplomats in Brussels told AFP.
EU ministers were set to also target the country's central bank, petrochemicals and gold.
The sanctions would make it even more difficult for Iran, OPEC's second largest producer, to be paid in foreign currency for its oil exports, worth more than 100 billion dollars in 2011.
Previous rounds of EU and US sanctions targeting Iran's financial system have already caused a shortage of foreign currency.
Tehran insists its nuclear work is designed to master civilian applications of the technology, despite suspicions in the West that Israel's arch-foe is developing an atomic weapons program.