WASHINGTON — The Federal Reserve on Monday issued a proposal that would force big U.S. banks to pay an annual fee to help cover the cost of regulating them.

Under the proposal, the Fed would look back and start the assessment for the 2012 calendar year, requiring about 70 financial firms to pay a total of $440 million.

It would not start collecting the payments until the rule is finalized. An asset-based formula would be used to determine each company’s assessment.

The 2010 Dodd-Frank financial reform law called on the Fed to issue such a proposal, to help the Fed cover the cost of enhanced supervision and regulation of bank holding companies, and savings and loan holding companies, with $50 billion or more in assets.

It also covers non-bank financial firms that will be designated as “systemic” by the Financial Stability Oversight Council, a council of regulators chaired by the U.S. Treasury secretary that watches the marketplace for emerging risks.

Designated firms will face heightened oversight by the Fed.

The Fed is accepting comments on the proposal until June 15.