Investors who were allegedly misled by Citigroup about a housing-related investment at the start of the mortgage meltdown lost more than $700 million in the deal, the Securities and Exchange Commission estimated in a court document filed Monday.

That figure is more than double the $285 million the SEC has said it would accept from Citigroup to settle the agency’s case against the firm. The SEC explained that all the investor losses were ”not necessarily” the result of misconduct.

The SEC disclosed its estimate in response to questions from U.S. District Court Judge Jed S. Rakoff, who must decide whether to approve the settlement.

The SEC recently charged that Citigroup Global Markets, a subsidiary of the bank, misled investors about a complex investment in 2007 that was tied to the collapsing housing market. The firm led investors to believe that an independent party chose the assets from which the instrument was created, but Citigroup actually “exerted significant influence” over those choices, the SEC alleged. Citigroup then successfully bet that the investment would lose value, profiting while the investors lost, the SEC charged.

Citigroup made profits of at least $160 million on the transaction, the SEC said.

The settlement with Citigroup calls for the firm to give up alleged ill-gotten gains of $160 million, plus pay interest of $30 million and a $95 million penalty, for a total payment of $285 million.

Under the proposed settlement, Citigroup neither admits nor denies wrongdoing.

The only Citigroup employee charged in the case was described by the bank as a mid-level employee at the subsidiary, and he is fighting the charges.

The case is one of several in which regulators allege that Wall Street firms left their customers holding the bag for investments tied to subprime mortgages. Rakoff has criticized past SEC settlements as inadequate, but he also has approved settlements that he faulted, including one with Bank of America.

An advocacy group called Better Markets called on Rakoff to reject the Citigroup settlement.

“Unfortunately, the SEC seems more interested in issuing press releases and wrapping up its investigations than punishing Wall Street for its massive frauds,” Dennis Kelleher, the group’s president, said in a statement.

“Such settlements don’t deter crime.  They reward it,” Kelleher said.

The settlement is modest in comparison to Citigroup’s profits, which totaled $3.8 billion in the third quarter of this year.

In its filing Monday, the SEC defended the settlement as “fair, adequate and reasonable.”

The SEC had previously told the court that the “extent of injury to innocent parties” was one of nine factors it considered in determining what penalty would be appropriate.

But in its filing Monday, the SEC said it “did not devote resources to calculating” how much money investors lost as a result of Citigroup’s conduct. The agency said it was not required to measure investors’ losses.

Rakoff, who has scheduled a hearing on the Citigroup settlement, has questioned several aspects of the case, including why the company was charged with negligent rather than reckless or intentional fraud.

The SEC said the evidence “did not clearly establish an intent to defraud.”

The SEC argued that the judge is not entitled “to evaluate claims that the government did not make and to inquire as to why they were not made.” Citing legal precedent, the SEC said courts “should pay deference” to the agency’s judgment.

The judge also questioned the SEC’s practice of letting defendants settle without admitting or denying wrongdoing. Citigroup said it made a business decision to settle, partly to avoid the risk of losing the case and having the outcome used against it in other lawsuits.

In a court filing, Citigroup also said that, without a settlement, the SEC would have to litigate “substantial factual and legal issues.” For example, marketing materials for the deal told investors that Citigroup “may be expected to have interests that are adverse to the interests of Noteholders.”