WASHINGTON — Years after Fannie Mae and Freddie Mac were found to have misrepresented their earnings by billions of dollars, a federal regulator is warning them to follow both the spirit and the letter of a new accounting rule.

The Office of Federal Housing Enterprise Oversight said it would consider taking action against the government-sponsored mortgage funding companies if their handling of the new rule raises concerns, even if their conduct “technically complies with the accounting standard.”

The OFHEO statement came less than a week after the regulatory agency said it found “certain issues” in Freddie Mac’s implementation of accounting standards which “raise concerns” about the company’s capital, the financial cushion it is required to maintain to protect against losses.

To reduce the risk of the companies becoming so weak that they are unable to meet their obligations without a bailout, the government requires them to operate with at least a certain amount of capital, determined by a federal formula.

The regulator noted last week that Freddie Mac’s approach to implementing the new accounting rule generated a $1 billion gain as of January 1, “providing an immediate boost to Freddie Mac’s regulatory capital.”