U.S. Steel and Japan’s Nippon Steel sued the United States government on Monday in a last-ditch attempt to revive their attempted merger after President Biden blocked it last week on the basis that the transaction posed a threat to national security.

The lawsuit, filed in a federal court in Washington, accused Mr. Biden and other senior administration officials of corrupting the review process for political gain and of harming steel workers and the American steel industry by blocking the deal under false national security pretenses.

Mr. Biden moved to block the merger after a government panel charged with reviewing foreign investments failed to reach a decision about whether the deal should proceed. In a statement on Friday, Mr. Biden said that he was acting to ensure that the U.S. maintains a strong domestically owned and operated steel industry. The president had previously vowed to ensure that U.S. Steel remained American-owned.

The companies are asking for the Committee on Foreign Investment in the United States to conduct a new review of the deal.

The companies also filed a separate lawsuit against Cleveland-Cliffs, an American steel company that previously tried to buy U.S. Steel but was rebuffed, along with Lourenco Goncalves, chief executive of Cleveland-Cliffs, and David McCall, international president of the powerful union United Steelworkers. The lawsuit alleged that Cleveland-Cliffs and the head of the union illegally colluded to undermine the proposed deal between U.S. Steel and Nippon Steel.

The legal actions represented a long-shot maneuver by the companies to preserve a deal that was ensnared in election year politics. Presidents have broad authority to determine what constitutes a national security threat, and no transaction blocked under those powers has ever been overturned by the courts.

However, Mr. Biden’s move to terminate Nippon’s $14 billion bid for U.S. Steel raised questions about whether those powers were being abused, given that Japan is a close ally of the United States. In the rare cases where deals have been blocked, they usually involved companies with ties to U.S. adversaries such as China.

“Nippon Steel and U.S. Steel are disappointed to see such a clear and improper exploitation of the country’s national security apparatus in an effort to help win an election and repay political favors,” the companies said in a statement on Monday. “Nippon Steel and U.S. Steel are entitled to a fair process and have been left with no choice but to challenge the decision and the process leading to it in court.”

David Burritt, the chief executive of U.S. Steel, assailed Mr. Biden on Monday, suggesting that the president blocked the deal because he “owed the union boss a favor in exchange for an endorsement.”

“The government failed us,” Mr. Burritt said in an interview on the Fox Business Network on Monday. “They failed because they didn’t follow the process, and we are going to right that wrong.”

The White House defended Mr. Biden’s decision on Monday, pointing to the threats to the U.S. steel industry that the committee highlighted.

“A committee of national security and trade experts determined this acquisition would create risk for American national security,” said Robyn Patterson, a White House spokeswoman. “President Biden will never hesitate to protect the security of this nation, its infrastructure, and the resilience of its supply chains.”

The lawsuit against the Biden administration was filed in the U.S. Court of Appeals for the District of Columbia Circuit. The suit also names Treasury Secretary Janet L. Yellen, who chairs the Committee on Foreign Investment in the United States, and Merrick Garland, the attorney general.

The companies argue that because Mr. Biden publicly said last March that he did not want the deal to happen, the national security review conducted by the panel, known as CFIUS, was tainted by politics and “designed to reach a predetermined result.” They also claimed that the panel had failed to engage with the companies when they proposed measures to mitigate any national security concerns.

After a yearlong review process, the interagency committee — ultimately divided on the risks posed by the transaction — left the decision to Mr. Biden, who had said that U.S. Steel should remain American-owned and -operated.

“It is my solemn responsibility as president to ensure that, now and long into the future, America has a strong domestically owned and operated steel industry that can continue to power our national sources of strength at home and abroad,” Mr. Biden said in a statement last Friday morning. “And it is a fulfillment of that responsibility to block foreign ownership of this vital American company.”

The committee was created in the 1970s to screen international mergers and acquisitions for national security concerns. Over the years the definition of national security has broadened, and in many cases the work of the panel has been consumed by political considerations, often with a focus on keeping Chinese investments out of America.

Since 1990, eight other foreign transactions have been blocked by presidents, according to the Congressional Research Service.

The companies are hopeful that a 2012 case involving a Chinese-owned company that tried to buy American wind-farm projects could provide an opening for more scrutiny of how CFIUS handled the steel deal. The Obama administration blocked that deal, but after the company filed a lawsuit an appeals court agreed that the company, Ralls Corporation, had a right to see and rebut certain evidence that was used to block the transaction.

The Obama administration and the company ultimately settled the lawsuit.

The legal challenge by U.S. Steel and Nippon is on different grounds than that case. If successful, this suit would herald sweeping changes to the authority of the U.S. government to vet foreign transactions.

While the Biden administration’s move won praise from the steelworkers union, it drew scorn from many economists and legal experts who warned that the president’s decision would deter foreign investment.

“What’s infuriating is that Biden claimed to stand for the rule of law and for our international alliances,” said John Kabealo, a Washington-based lawyer who specializes in cross-border transactions. “He told voters ad nauseam that Trump was xenophobic and self-dealing, and now he slaps one of our most important allies in the face on the thinnest of pretenses.”

Although President-elect Donald J. Trump has previously said that he would block the Nippon bid, the companies have remained hopeful that he might reconsider that position if given the opportunity to help broker a satisfactory deal.

But on Monday, Mr. Trump made clear that he still does not want U.S. Steel to be sold.

“Why would they want to sell U.S. Steel now when Tariffs will make it a much more profitable and valuable company? Mr. Trump wrote on social media. “Wouldn’t it be nice to have U.S. Steel, once the greatest company in the World, lead the charge toward greatness again?”