A federal judge who has accused the Securities and Exchange Commission of negotiating weak settlements in Wall Street cases on Thursday accused the agency of misleading a federal appeals court.

U.S. District Court Judge Jed S. Rakoff said the SEC also withheld from him important information that he needed to do his job.

Rakoff spelled out his allegations in an order that he said was intended to inform the appeals court and prevent anything similar from happening in the future.

Meanwhile, the SEC took the dramatic step of asking the U.S. Court of Appeals for the 2nd Circuit to overrule a recent Rakoff decision by issuing a special writ generally reserved for cases in which a judge has grossly overstepped his bounds. Called a writ of mandamus, such a direct and personal challenge to a judge is far from a routine gambit.

The judge and the SEC are locked in an extraordinary battle over how the government should police financial fraud, and just when it seemed that the conflict could not get more contentious, Thursday’s development added a dimension.

Rakoff, who presides over major Wall Street cases from his bench in Manhattan, has been pushing the SEC to stop negotiating settlements in which firms accused of securities fraud neither admit nor deny wrongdoing. In a recent case involving a Citigroup mortgage deal in which investors allegedly lost more than $700 million, he rejected a settlement under which Citigroup would pay $285 million, saying it was “neither fair, nor reasonable, nor adequate, nor in the public interest.”

Companies can look upon such settlements as “a cost of doing business,” he wrote.

The SEC says that instead of admitting wrongdoing, defendants would fight the agency all the way to trial, tying up resources that regulators need to investigate other cases. The SEC has asked an appeals court to throw out Rakoff’s ruling, and on Tuesday it filed an “emergency” motion asking the appeals court to freeze Rakoff’s hand in the Citigroup case while the appeal is pending.

In his order Thursday, Rakoff accused the SEC of misleading the appeals court and leaving him in the dark when it made its emergency request.

The SEC told the appeals court that Rakoff had given Citigroup until Jan. 3 to answer or move to dismiss the SEC’s complaint. If the appeals court did not intervene, the SEC said, the settlement could be torpedoed and the agency could be irreparably harmed because Citigroup could be prompted to deny the charges.

“This statement would seem to have been materially misleading in at least four respects,” Rakoff wrote Thursday.

First, Rakoff wrote, a motion by Citigroup to dismiss the case would focus on legal issues and would not involve an admission or denial of the allegations.

“Second, as a factual matter, the SEC was either already aware that Citigroup was planning to move to dismiss rather than to answer . . . or could have readily found this out by calling counsel for Citigroup,” Rakoff wrote.

Third, Rakoff said, in his court, neither the SEC nor Citigroup had argued that the Jan. 3 deadline was significant. And, fourth, Rakoff said, the SEC “was under a professional obligation to bring to the attention of the Court of Appeals” a Supreme Court ruling that undercut its arguments.

The SEC told the appeals court that it had asked Rakoff to put the case on hold but had not gotten an answer from the judge. Rakoff complained that the SEC knew his opinion was not due before Dec. 30, and he wrote that he spent the Christmas holiday working on it.

The judge said the SEC and Citigroup called him Monday afternoon to discuss Citigroup’s planned motion to dismiss, and during that conversation never mentioned that the SEC had asked the appeals court for the emergency stay hours earlier.

According to Rakoff’s statement on Thursday, he missed his chance to make his own views known to the appeals court before it granted the SEC a temporary stay late Tuesday. He also issued the opinion he had spent the holiday preparing “totally unaware of any of the filings in the Court of Appeals.”

By failing to put him on notice about the emergency request, Rakoff wrote, the SEC and Citigroup “held back from this Court material information it needed to do its job.”

In a statement, SEC spokesman John Nester said the agency “will respond as appropriate in the proceedings before the Court of Appeals.”