The SEC has rejected a proposal by its own enforcement staff to settle a landmark case in which the agency is trying to force a former corporate chief executive to give up millions of dollars in bonuses and stock profits he received while the company was cooking its books.

The plan to settle for significantly less money than the agency originally sought posed a test question for the Securities and Exchange Commission: Was the staff letting the former executive off the hook too easily?

Or was the agency being overzealous when it brought the case in the first place?

Both sentiments combined to torpedo the deal when the commissioners weighed the proposal last week, according to a source close to the matter.

The case involves Maynard L. Jenkins, former chief executive of CSK Auto, an Arizona-based auto-parts retailer that had to correct years of financial statements.

In 2009, the agency sued Jenkins, saying he should repay the auto parts retailer more than $4 million that he reaped while the company was “engaged in a pervasive accounting fraud.”

Jenkins, however, was not personally charged with fraud.

It was the first time the SEC had filed a so-called clawback suit to wrest money from an executive who was not accused of complicity in accounting fraud.

The SEC was using the watershed Sarbanes-Oxley law enacted in 2002 in response to accounting scandals at companies such as Enron and WorldCom.

The law calls for chief executives and chief financial officers to forfeit stock profits or bonuses they receive while their company is misleading the public about its financial performance.

He and the SEC staff notified the trial court in March that they had reached a tentative settlement, subject to approval by the SEC’s governing commissioners.

On Monday, they notified the court that their efforts “have not been successful.”

The proposed settlement was for less than half the amount the SEC originally sought, according to a second source familiar with the matter.

Jenkins and the staff thought the deal was in both his interest and that of the agency, but a bipartisan majority of the SEC’s commissioners disagreed, the first source said. Both spoke on condition of anonymity because the information involved internal SEC deliberations.

“We cannot comment on Commission deliberations, but we will continue to pursue the case vigorously,” SEC spokesman Kevin J. Callahan said by e-mail.

John W. Spiegel, a lawyer for Jenkins, declined to comment.

The law’s clawback provision was meant to hold top executives accountable for fraud and to prevent them from profiting from it. It can encourage executives to be vigilant, but it can also penalize executives who had nothing to do with the wrongdoing.

The objective is to reimburse the company and shareholders. But it can cost companies money to recoup money.

In a January court filing, CSK Auto said it is responsible for Jenkins’s legal costs. The company has been billed “approximately $1.9 million in legal fees and costs associated with Mr. Jenkins and $1.5 million since litigation commenced” in the SEC’s case against him, according to a court filing by Jeffrey L. Groves, general counsel of CSK’s parent company, O’Reilly Automotive.

Those costs have been covered by an insurer for CSK, according to another court document.

Jenkins is 68 and in declining health, his lawyers said in a January court filing.

The SEC lawsuit has left him in financial limbo, they wrote. As long as it remains unresolved, he “cannot plan financially for his future and that of his family,” they said.

His defense team has argued that the SEC “is attempting to impose a Draconian penalty on an admittedly innocent person.”

“The SEC’s nonsensical view is that Mr. Jenkins must pay (literally and figuratively) for . . . misconduct by others because he was the ‘captain of the ship,’ despite the fact that under its own view of the evidence, his crew was mutinous,” his lawyers have argued.

The rejection of the settlement came soon after the SEC took flak for a settlement in which it fined J.P. Morgan Securities but took no action against any of the firm’s employees or executives.

In another case, SEC Commissioner Luis A. Aguilar last week took the extraordinary step of publicly dissenting from an SEC enforcement action on the grounds that it was too weak.

The rejection of the Jenkins settlement sets the stage for a civil trial.

Barring a new settlement, the case will test the SEC’s application of the clawback law, and it will call on the agency to prove that CSK’s accounting involved “misconduct” rather than innocent error.

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