New York's financial regulator has called on firms to submit proposals to set up "regulated" exchanges for digital currencies like Bitcoin.
The state's Department of Financial Services (NYDFS) said it wanted to better protect consumers, and prevent money-laundering.
It comes as a top Bitcoin exchange, Mt Gox, filed for bankruptcy last month.
Bitcoins have been gaining in popularity recently, but they are not governed by any financial regulator.
"The fact is that virtual currencies are unlikely to disappear entirely," said Benjamin Lawsky, New York's superintendent of financial services.Continue reading the main story
The recent problems at Mt Gox and other firms further demonstrate the urgent need for stronger oversight of virtual currency exchanges”End QuoteBenjamin LawskySuperintendent of Financial Services, New York
"As such, turning a blind eye and failing to put in place guardrails for virtual currency firms while consumers use that product is simply not a tenable strategy for regulators."'Stronger oversight'
The lack of any regulatory control or oversight of Bitcoins has triggered concerns on various fronts.
It is difficult to trace transactions carried out using Bitcoins - one of the factors behind their popularity - and the currency has been linked to illegal activity online.
Bitcoins are also seen by some as a route for tax evasion and money laundering.
Russia has declared transactions using the digital currency illegal, China has banned its banks from handling Bitcoin trades, and there have been calls for the US to do the same.
Singapore has imposed a tax on Bitcoin trading and using it to pay for services, after classifying it as goods, rather than a currency.
Earlier this month, the Japanese government also said Bitcoin is not a currency and that some transactions using the virtual unit should be taxed.
The collapse of Mt Gox has only added to the concerns.
The firm filed for bankruptcy in Japan in February after losing about $473m (£284m) worth of customers' bitcoins to what it says was a hacking attack.
"The recent problems at Mt Gox and other firms further demonstrate the urgent need for stronger oversight of virtual currency exchanges," said Mr Lawsky.
"Consumers should understand and receive appropriate disclosures about the potential risks associated with using virtual currencies or any other financial product."