The action came after Senator Chuck Schumer, the New York Democrat and minority leader, said he would block Mr. Trump’s nomination of Mr. Clayton, 58, for the U.S. attorney post, using a prerogative given to home-state senators. Mr. Schumer made his move after weeks in which some liberal Democrats had made scathing attacks on him for doing too little to resist Mr. Trump.

Mr. Trump said in his Truth Social post that he would continue to pursue Mr. Clayton’s Senate confirmation. Mr. Clayton, a lawyer at the firm Sullivan & Cromwell who has never been a prosecutor, served as chairman of the Securities and Exchange Commission from 2017 to 2020.

“During my first term, Jay served with great distinction as the chair of the Securities and Exchange Commission, and earned the respect of everyone,” Mr. Trump said in the post.

The Southern District, which is based in Manhattan, has long been considered one of the most prestigious federal prosecutor’s offices in the country. It is known for handling high-profile cases involving public corruption, national security, international terrorism, fraud on Wall Street and other white-collar crime and sex trafficking.

The district, which includes Manhattan, the Bronx and several upstate counties, has long been referred to jokingly as the Sovereign District, a nod to its prized past independence. Its alumni have included former U.S. attorneys general, F.B.I. directors and countless judges.

In 2018, the office brought charges against Michael D. Cohen, Mr. Trump’s former lawyer and fixer, for paying a porn star to keep her quiet during the 2016 presidential campaign about a sexual encounter she said she had with Mr. Trump. Mr. Cohen went to prison. It is known Mr. Trump was also under scrutiny by the office as part of the investigation; he was never charged.

But since Mr. Trump took office, the Southern District has experienced turmoil and upheaval, with his Justice Department orchestrating the dismissal of the office’s most prominent case, the prosecution of Mayor Eric Adams of New York City. It did so over the objection of Danielle R. Sassoon, then the office’s interim leader, who resigned. At least one other senior prosecutor also resigned, and still others have been placed on administrative leave.

Since Ms. Sassoon’s resignation, Matthew Podolsky, who spent a decade prosecuting prominent public corruption and securities fraud cases, has led the office as the acting U.S. attorney.

Mr. Trump first announced in mid-November that he would nominate Mr. Clayton for the permanent job, calling him “a highly respected business leader, counsel and public servant.”

In his social media post, the president noted that Mr. Clayton had been “previously confirmed by the Senate on a bipartisan basis,” a reference to his S.E.C. appointment.

During Mr. Clayton’s leadership of the S.E.C., the agency sued Elon Musk, the tech billionaire who is currently a top adviser to Mr. Trump, accusing him of securities fraud. Mr. Musk paid a $20 million fine and stepped aside as chairman of Tesla for three years to resolve the case.

Mr. Trump’s announcement Wednesday came on the same day that Mr. Schumer said he would block the appointment of Mr. Clayton and Joseph Nocella Jr., Mr. Trump’s pick to lead the Eastern District of New York. Mr. Schumer was using an arcane Senate provision, known as a “blue slip,” in which senators can refuse to consent to the nominations of U.S. attorneys in their state.

The tradition, which dates to the early 1900s, has frequently been used by home-state senators to block the nominations of federal prosecutors, judges and U.S. marshals.

Mr. Trump has not made a similar interim appointment of Mr. Nocella, who worked as an assistant U.S. attorney in the Eastern District in the 1990s and has most recently served as a Long Island district court judge.

Republicans on the Senate Judiciary Committee have said they support continuing to honor the blue-slip tradition, even if it means that their preferred nominees will potentially be blocked by Democrats.

“It serves a useful purpose even when in Democratic hands,” said Senator John Cornyn, Republican of Texas.