Donald J. Trump on Wednesday lost his initial bid for a New York appeals court to pause the more than $450 million judgment he faces in a civil fraud case, exposing him to potential financial peril.

Mr. Trump told the appeals court that it was “impossible” to secure a bond of more than $450 million — any company providing a bond would most likely require the former president to pledge cash and other collateral — and offered to post one of only $100 million. Any bond that the appeals court accepts would prevent the New York attorney general’s office, which brought the case, from collecting from Mr. Trump while he appeals.

In court filings, Mr. Trump’s lawyers said he might need to sell some properties at fire-sale prices unless the court cuts him a break, a stunning acknowledgment of his financial limitations.

Yet the former president might still avoid that costly outcome.

Wednesday’s ruling came from a single appellate court judge assigned to consider Mr. Trump’s emergency request. Mr. Trump can try again with a panel of five appellate court judges, which next month will entertain his request to pause the judgment and accept a smaller bond.

For now, the initial ruling is a setback for Mr. Trump, who is racing the clock. If he ultimately fails to secure a bond, the attorney general, Letitia James, could seek to collect from him at any moment. Although the office is expected to provide a 30-day grace period that would expire on March 25, it has the power to move swiftly to seize Mr. Trump’s bank accounts and potentially take control of his New York properties.

However the case is resolved, Mr. Trump’s request for relief represented a humbling concession from a man whose public image is synonymous with wealth. His conspicuous displays of gold-plated luxury underpinned his rise to tabloid fame, a stark contrast with the current spectacle of him scrambling to avert financial peril.

A lawyer for Mr. Trump, Christopher M. Kise, did not immediately respond to requests for comment.

In seeking relief, Mr. Trump’s lawyers disclosed that he would be unable to secure a bond for the full $454 million. Under New York law, a defendant also owes 9 percent interest to the plaintiff until the judgment is paid or the appeal resolved, meaning a full bond might reach $500 million or more.

“The exorbitant and punitive amount of the judgment coupled with an unlawful and unconstitutional blanket prohibition on lending transactions would make it impossible to secure and post a complete bond,” the lawyers wrote.

They also asked the appeals court to delay a wide range of other punishments that the trial judge in the fraud case, Arthur F. Engoron, levied in a decision this month. They include a prohibition on obtaining a loan from a New York bank for three years and a ban on running a company in the state during that same period.

The appellate court judge assigned Wednesday to consider Mr. Trump’s filing, Anil Singh, granted the former president’s request to temporarily pause those punishments, a decision that could help him obtain a loan or a bond.

Financial relief might also come from a separate deal: Mr. Trump’s stake in Trump Media & Technology Group, his social media company, could be worth up to $4 billion after a long-delayed merger is made final this year, though it won’t be in time for Ms. James’s March 25 deadline.

In its own filing, Ms. James’s office asked the appeals court to deny Mr. Trump’s request.

“There is no merit to defendants’ contention that a full bond or deposit is unnecessary because they are willing to post a partial undertaking of less than a quarter of the judgment amount,” the attorney general’s office wrote. “Defendants all but concede that Mr. Trump has insufficient liquid assets to satisfy the judgment.”

Ms. James built her case on the accusation that Mr. Trump had fraudulently inflated his net worth by as much as $2 billion. He did so, Ms. James argued, to obtain favorable loans and other financial benefits.

Justice Engoron sided with Ms. James, concluding that Mr. Trump defrauded his lenders, who had expected him to maintain a certain net worth.

Mr. Trump’s net worth is largely derived from real estate, and the sum of the judgment in the civil fraud case and the $83.3 million judgment he faces from a defamation trial involving the writer E. Jean Carroll eclipses his stockpile of cash.

As of last year, Mr. Trump was sitting on more than $350 million in cash, as well as stocks and bonds he could sell in a hurry, according to a recent New York Times review of his financial records.

Mr. Trump appears to be struggling to line up a bond in the defamation case as well. He has until early next month to do so, and his lawyers recently asked a judge to either grant him more time or reduce the size of the bond.

A bond, in simplest terms, is a document that a company provides to the court on a defendant’s behalf. The bond company promises the court to cover a judgment if a defendant, in this case Mr. Trump, loses an appeal and fails to pay.

In exchange, Mr. Trump would have to pay the bond company a premium fee, typically anywhere from 1 to 3 percent of the judgment. Mr. Trump would also have to pledge collateral to the bond company, offering it cash, stocks and bonds.

Although each deal is different, companies offering appeal bonds might be unwilling to take Mr. Trump’s property as collateral, especially if a building already has a mortgage, experts said.

Legal experts predicted that even if Mr. Trump loses before the five-judge appellate panel he might still come up with a larger bond, noting that his lawyers did not characterize the $100 million bond as the only possible outcome.

The $100 million bond “resembles an opening real estate bid,” said Mark Zauderer, a partner at the law firm Dorf Nelson & Zauderer who is a veteran New York business litigator and has secured many appeal bonds. “But here, the negotiation will end, because it is the court that will determine the actual dollar amount of security, not Trump.”