Bitcoin was created over a decade ago but came to wider attention in late 2017 when its value surged to almost US$20,000 ($29,313). Its value has since plummeted, adding to fears that it is too risky among regulators, investors and bank bosses.
JP Morgan boss Jamie Dimon last year said he regrets calling Bitcoin a "fraud", but added that he still had no interest in it.
As well as calling on the European Commission to consider a pan-European law for the industry, the EBA also criticised the energy consumption required for some crypto-asset activity. It said this should be looked at in light of the EU's sustainability targets.
Bitcoin, for example, uses huge amounts of electricity - equivalent to the energy consumption of Hong Kong, Singapore and Portugal - to maintain its network.
The lack of regulation for the cryptocurrency industry has been a concern for some time. In the UK, the Treasury, Bank of England and Financial Conduct Authority have pledged to take steps in the coming months to address the threats posed.
On Tuesday, the Governor of the Bank of England said the central bank is upgrading its technology systems to that they are able to work with cryptocurrencies.
In an online question and answer session on the future of money, Mark Carney said that the Bank does not think cryptocurrencies are an effective form of currency due to their volatility. He cited the 40 per cent drop in Bitcoin's value over a fortnight in November.
However, he said he is "open minded" about the possibilities of distributed ledger technology (DLT), the system by which Bitcoin and other cryptocurrencies store information about who owns what.
He said DLT, which includes Bitcoin's blockchain, could "serve the public better" than current payments systems, which "must now evolve to meet the demands of fully reliable, real-time, distributed transactions".
"People are increasingly forming connections directly, instantaneously and openly, and this is revolutionising how they consume, work, and communicate," said Mr Carney. "Yet the financial system continues to be arranged around a series of hubs and spokes like banks and payments, clearing and settlement systems.
"[DLT] is throwing down the gauntlet to the existing payment systems."
However, the Bank is also looking into whether cryptocurrencies could destabilise the financial system, Mr Carney added. He said he believed this is unlikely since cryptocurrencies make up less than 1 per cent of global GDP, but the Bank is investigating nonetheless.
Carney also reiterated the Bank's enduring support for cash payments, even as their popularity diminishes.
One in ten people use ApplePay to make the majority of their transactions, according to a survey by the Bank. A further six in ten mainly use card payments, with the remainder relying mostly on cash.
Carney said the Bank's support for maintaining physical cash is evident in its recent announcement of plastic £50 notes ($94) , which will sport the face of a British scientist.
