House Republicans reacted with outrage on Thursday night to the federal indictment of former President Donald J. Trump, vowing to use their majority in Congress to fight the Justice Department.

“WITCH HUNT,” was posted on the Twitter account of the Republican-led House Judiciary Committee within minutes of news of the indictment becoming public.

The chairman of that panel, Representative Jim Jordan of Ohio, has used his perch to attempt to pressure the Justice Department over what he views as unfair treatment of Mr. Trump. Mr. Jordan this week sent a letter to Attorney General Merrick Garland demanding unredacted documents concerning the investigation of the special counsel, Jack Smith.

“It’s a sad day for America,” Mr. Jordan said in a statement on Thursday. “God bless President Trump.”

Members of Congress have no power to stop criminal charges, but they can attempt to interfere with prosecutors through their legislative powers, such as issuing subpoenas, demanding witness interviews or documents, restricting Justice Department funding and using the platform of their offices to attempt to publicly influence the case.

Several Republicans who are closely allied with Mr. Trump said, without evidence, that the indictment was an attempt to distract from their investigation into President Biden’s family, including his son Hunter’s business dealings. They made clear that they would target federal law enforcement in retaliation.

Representative Marjorie Taylor Greene, Republican of Georgia, said the case against Mr. Trump was a “stain on our nation that the F.B.I. and D.O.J. are so corrupt and they don’t even hide it anymore.” She added, “We must win in 2024. We must beat these sick people.”

Representative Matt Gaetz, Republican of Florida and one of Mr. Trump’s closest allies, predicted that the former president would prevail against the charges, and that his rivals would be imprisoned.

“This scheme won’t succeed. President Donald Trump will be back in the White House and Joe Biden will be Hunter’s cellmate,” Mr. Gaetz wrote on Twitter.

It was the second time this year that House Republicans rallied to Mr. Trump’s defense after he was charged criminally. In April, Speaker Kevin McCarthy pledged to use the investigative powers of the House to hold Alvin L. Bragg, the Manhattan district attorney, “accountable” after Mr. Trump was charged in New York with 34 counts of falsifying business records.