A day after the CEO of a Bitcoin exchange company was arrested for money laundering in New York City, a top New York state regulator suggested that more regulations would be in store for the digital currency in the near future.

Speaking at a hearing on Bitcoin, New York Department of Financial Services head Benjamin Lawsky said that he would put forward a "proposed regulatory framework" for virtual currencies such as Bitcoin in 2014, acknowledging that the new technologies are "uncharted waters" for regulators.

Part of that regulation, Lawsky said, could be "BitLicenses" for businesses trading in virtual currencies.

Tuesday's hearing brought together investors in Bitcoin and related businesses, including the Winklevoss twins, who are famous for their role in the founding of Facebook and now invest in Bitcoin and design financial products for digital currencies. Tyler Winklevoss called Monday's arrest of Charlie Shrem for money laundering with Bitcoins a "speed bump" on the road to the currency's legitimacy. Other investors stressed that Lawsky and other regulators should be careful not to over-regulate digital payments systems and in doing so damage their benefits, which they said include low transactions costs.

Lawsky at one point warned the group that money laundering, such as what happened with the Silk Road online drug bazaar that dealt in Bitcoins and was shut down last year, was not worth "allowing 1,000 flowers to bloom on the innovation side" of alternative currencies.

Tuesday's hearings will be followed by another set on Wednesday. In the fall, the federal government also held a series of hearings on digital currencies, including one before the Senate Homeland Security and Governmental Affairs Committee that Bitcoin advocates generally thought went well. No lawmakers or federal regulators proposed new rules for alternative currencies following those hearings.