President Donald Trump threatened Wednesday to “get involved” in an escalating fight between conservative House Republicans and Deputy Attorney General Rod Rosenstein.

“A Rigged System — They don’t want to turn over Documents to Congress,” Mr. Trump Tweeted. “What are they afraid of? Why so much redacting? Why such unequal ‘justice?’ At some point I will have no choice but to use the powers granted to the Presidency and get involved!”

The tweet inserts the President into a contentious battle between the conservative House Freedom Caucus led by Rep. Mark Meadows, North Carolina Republican, and Mr. Rosenstein, who oversees special counsel Robert Mueller’s Russia Investigation.

Mr. Trump tweeted just hours before multiple news outlets reported the Justice Department declined to provide lawmakers in the House Freedom Caucus with an unreacted memo authored by Mr. Rosenstein outlining the full scope of Mr. Mueller’s Russia investigation. Republicans in Congress have demanded to know the probe’s scope and whether Mr. Mueller is working outside of it.

Assistant Attorney General Stephen Boyd said in a letter Wednesday that turning over the memo would “threaten the integrity” of Mueller’s investigation, the reports said.

“Although we are working to accommodate the requests of the House Oversight and Government Reform Committee in a number of oversight matters, we cannot provide the requested information pertaining to the Special Counsel’s ongoing investigation consistent with longstanding principles of investigatory independence,” Mr. Boyd wrote, according to news reports.

A redacted version of the memo was disclosed in August court filings. The public version states Mueller has the authority to investigate whether Trump campaign officials’ “committed a crime or crimes by colluding with Russian government officials.”

On Monday it was revealed that members of the House Freedom Caucus drafted articles of impeachment against Mr. Rosenstein. The lawmakers accuse the Justice Department’s second-in-command of refusing to comply with a subpoena to hand over documents to two Congressional committees.

The documents are related a Foreign Intelligence Surveillance Act (FISA) warrant on Trump campaign aide Carter Page ahead of the 2016 presidential campaign. Mr. Rosenstein renewed the FISA warrant on Mr. Page that was previously signed off on by former FBI Director James B. Comey, former FBI Deputy Director Andrew McCabe, former Acting Attorney General Sally Yates and others then at the Justice Department.

House Freedom Caucus members accuse Mr. Rosenstein of abusing his authority when he renewed the FISA warrant for Mr. Page. They also alleged Mr. Rosenstein has slow-walked handing those documents over to the House Judiciary and House Oversight and Government Reform committees, which had requested them.

Mr. Rosenstein fired back at the conservative lawmakers Tuesday, calling the impeachment effort an “extortion” attempt.

“There have been people who have been making threats privately and publicly against me for quite some time, and I think they should understand the Department of Justice is not going to be extorted,” he said. “We are going to do what is required by the rule of law and any kind of threats anybody makes are not going to affect the way we do our job.”

The Justice Department has said it is complying with the document requests, but the sheer volume of pages and redactions have slowed the process. Last week, the chairmen of the the Judiciary and Oversight committees said they reached an agreement with the Justice Department over document production.

Mr. Trump is said to have privately debated firing Mr. Rosenstein, a frequent target of the president both in public comments and on Twitter. That anger stems from Mr. Rosenstein’s role in the Russia probe, which he inherited after Attorney General Jeff Sessions recused himself, and the renewing the Page FISA warrant.

Democrats and opponents of the president have said his attacks on Mr. Rosenstein are an effort to undercut Mr. Mueller’s probe.