Proposed changes to EU law would force companies that transfer Bitcoin or other crypto-assets to collect details on the recipient and sender.
The proposals would make crypto-assets more traceable, the EU Commission said, and would help stop money-laundering and the financing of terrorism.
The new rules would also prohibit providing anonymous crypto-asset wallets.
The proposals could take two years to become law.
The Commission argued that crypto-asset transfers should be subject to the same anti-money-laundering rules as wire transfers.