By Manu Raju and Jeremy Herb, CNN

(CNN) -- Republicans angry with the Justice Department over not providing documents to Congress are urging President Donald Trump to intervene in the latest dispute between House Intelligence Chairman Devin Nunes, a California Republican, and Attorney General Jeff Sessions.

Nunes threatened on Fox News over the weekend to hold Sessions in contempt after the Justice Department said it would not comply with his subpoena sent last month about records tied to the Russia investigation and the Foreign Intelligence Surveillance Act.

The move could give Trump a new reason to take aim at his attorney general, a frequent punching bag of the President's for recusing himself from overseeing the Russia investigation. If Sessions doesn't comply, Democrats fear it would give Trump new reason to fire his attorney general and appoint a replacement who would be in charge of special counsel Robert Mueller's investigation.

Rep. Pete King, a senior GOP member of the House Intelligence Committee, told CNN Tuesday that "they have to turn over documents," referring to the Justice Department. If not, he said Trump "should order them to."

"All I can say is the Justice Department has to turn over the documents," King told CNN. "And the President can decide whether it should or not. The President should make that decision."

Rep. Mark Meadows, who heads the conservative House Freedom Caucus and who frequently speaks with Trump, said either Sessions or Deputy Attorney General Rod Rosenstein "should be held in contempt of Congress" if "we don't get the documents."

"We have a legitimate request that has been made to the Department of Justice and the FBI, and we have them saying that they will not comply," Meadows said. "So we have two branches that are at odds. Last time I checked, the laws are on our side."

Nunes told reporters Monday he still had to talk to Sessions about the document request, but as of Tuesday afternoon, the two still have not spoken about it, according to a source familiar with the matter.

And despite the Justice Department making it clear last week that it had consulted with the White House and other agencies about the request, Nunes said he didn't think that the White House was on the same page as the department about the need to comply with the subpoena.

Nunes hasn't spoken with House Speaker Paul Ryan, but said he was confident contempt would move forward if the Justice Department didn't provide the documents.

"It wasn't a threat," Nunes said Monday. "It's what's going to happen."

Ryan on Tuesday declined to weigh in on contempt, but said that Congress expects its oversight requests to be complied with.

"I haven't spoken with Devin about this," Ryan said. "We have a thorough process we go through, but we clearly expect the administration to honor our document requests."

The push comes after a top White House aide, Marc Short, told CNN Monday evening that the White House would likely side with Sessions over the House GOP in the fight to hold the attorney general in contempt.

"I think we are supportive of our Cabinet," Short said.

Meadows pushed back.

"The last time I checked Marc Short was never elected to office," he said.

The Justice Department bluntly warned Nunes last week that giving the Hill access to the documents would amount to a national security risk, saying they pertain to a specific individual and doing so could lead to the loss of lives. Sessions sided with that view Monday evening when asked at a news conference in San Diego.

Republicans, however, are unmoved.

"I don't believe that ... Because I know what's in there, and I don't believe it," King said, referring to the Justice Department warning that the disclosure would put lives at risk.

It's unclear what precisely the classified House GOP subpoena pertains to, but King said "it involves abuses" with FISA.

The subpoena from Nunes is only the latest in a series of fights between House Republicans and the Justice Department over documents, including spats over the FISA application for former Trump campaign aide Carter Page and copies of the memos drafted by former FBI Director James Comey.

Another fight is brewing over the August 2017 memo Rosenstein sent to Mueller outlining the scope of the special counsel probe. A redacted version was made public in former Trump campaign chairman Paul Manafort's court case, and Meadows and fellow House Freedom Caucus member Jim Jordan, an Ohio Republican, pressed to see the full unredacted memo.

The Justice Department denied that request last week, but Jordan noted that now the judge in Manafort's case in Virginia has also demanded access to the document.

"Mark and I sent a letter five weeks ago wanting to see the August 2nd memo unredacted, and shazam — last week a federal judge says he wants to see the August 2 memo unredacted," Jordan said. "So it's not just Congress asking this, it's the judiciary branch as well now."

That judge ordered the document be produced under seal, which would mean members of Congress requesting to it would not see it under that order.