Rep. Jim Himes, a Connecticut Democrat, told reporters they heard from committee staff about the documents, but he declined to get into the details of what they show. Nunes has weathered a storm of calls for him to recuse himself from the Russia investigation since it was discovered that two White House aides coordinated the release of the information to him.
Himes also said that the committee has agreed to call FBI Director James Comey and NSA Director Mike Rogers back before the committee to testify again, but has not yet agreed on a time.
Democratic Rep. Mike Quigley said on CNN's "Erin Burnett OutFront" that he had also been briefed on the documents and suggested the White House was using them to distract and should consider declassifying them.
"If the White House is so concerned about this, they can tomorrow declassify those documents," Quigley said. "Clearly this is more about distracting."
The House investigation has been rocked by chaos in the two weeks since Comey announced that the FBI has been investigating possible collusion between top aides on the campaign of President Donald Trump and Russian officials who sought to sway the US election.
One day after that stunning revelation, Nunes secretly visited the White House to review evidence
that is now at the center of Trump's counter-offensive. The ensuing chaos rocked the House investigation and led some lawmakers to declare it dead, but Republicans and Democrats have slowly been setting it back on course.
House Speaker Paul Ryan appeared to put his own investigators on notice Tuesday when asked about calls for Nunes to recuse himself.
"I'll just say this. Chairman Nunes has my confidence. I've met with the committee. They have my confidence," Ryan said. "What's important is that this committee does its investigation on a bipartisan basis to get to the bottom of things and go investigate all things Russia. That's what this committee is going to do."
Nunes said late Monday that investigators had agreed on the list of witnesses they plan to interview. GOP Rep. Peter King suggested Tuesday the committee has agreed to bring in key figures who worked with the Trump campaign and were in communication with Russian officials.
The four top targets of the federal probe -- former Trump campaign chairman Paul Manafort, former Trump foreign policy adviser Carter Page, former Trump adviser Roger Stone and former National Security Adviser Michael Flynn -- have all offered to speak before
House and Senate investigators. But Flynn's lawyer has said that Flynn would only testify with a promise of immunity
from prosecution -- something no one has agreed to yet
"We certainly made a lot of progress. we've exchanged witness lists," Rep. Adam Schiff, the committee's top Democrat, told CNN's Wolf Blitzer Tuesday. "I think we're near agreement on bringing in both the witnesses that we want and the witnesses Nunes wants. Prior to doing that, we need to get the documents from these witnesses so that we'll understand what questions we want to ask. Obviously some of these folks we may only get one crack at."
Nunes said they could begin bringing in witnesses in as soon as two weeks from now, but cautioned that was an optimistic timeline and that Democrats have not yet agreed on a schedule.
Meanwhile, the Senate intelligence committee has started interviewing witnesses for its own Russia investigation this week, Senate intelligence Chairman Richard Burr said Tuesday.
Investigators are working together again one week after the lead Democrat on the investigation, Schiff, called for Nunes to recuse himself
because of his clandestine trip
to the White House two weeks ago.
Trump and his supporters have mounted an aggressive defense against the Russia investigations in public, trying to push the focus away from his own aides ties to Russia and instead toward reports from Bloomberg
and Fox News
that former National Security Adviser Susan Rice revealed the names of Trump transition aides collected in surveillance of foreign officials. Rice has not responded to CNN request for comments those reports, but she denied to MSNBC unmasking Trump transition aides and called the allegations against her as "absolutely false."
Burr's committee has 20 witnesses it plans to call, and Rice is currently not among those expected to testify. But the North Carolina Republican said that he's interested in bringing her in if the investigation goes in that direction.
"If there is intelligence that leads to a reason for us to look at Susan Rice then we will do it," Burr said. "I don't do it from news reports, but we will look at all the intelligence as we go through this investigation, whether Susan Rice or anybody, if there's intelligence leads to some value at bringing them in and having them in for an interview we will invite them in."
Democratic senators came to Rice's defense, with Sen. Dianne Feinstein of California saying that seeking to unmask US officials for national security purposes amounted to "regular order."
"I don't find that surprising at all," Feinstein said.
The steady stream of stories about Trump aides' ties to Russia has only continued. The Washington Post reported Monday
that Republican powerbroker and Trump supporter Erik Prince was engaged in an effort to create a backchannel for Trump to Russian President Vladimir Putin, meeting with a United Arab Emirates intermediary on the African island of Seychelles this past January. Both the White House and Prince deny this was on behalf of the Trump administration.
Nunes repeatedly declined to comment on whether he thought Rice was the source of the unmasking in reports that he viewed two weeks ago, or if he had any evidence that shows Rice is the source. He also declined to comment on the Seychelles report from the Post.
But the wounds surrounding his committee of the last two weeks have hardly healed -- behind the scenes, lawmakers have expressed skepticism with each new report that comes out, saying they want to review the evidence for themselves.
Schiff said that House and Senate investigators will soon have access to the intelligence he, Nunes and the White House have reviewed. He fought back Tuesday against the new line of attack from the White House, saying that Nunes and the White House still need to explain why they concealed their roles in the release of this intelligence.
"This action is long overdue and follows an inexplicable series of events in which the White House played a role in selectively and surreptitiously providing the documents to our Chairman (Nunes)," Schiff said in a statement. "The White House has yet to explain why it attempted to conceal its role in the compilation of these materials. The White House is not a whistleblower and nothing that I was shown justifies such duplicitous conduct."
Schiff also pushed back on Trump's allegations about Rice, hinting that the White House should show the documents to the public and saying that incidental collection routinely involves the collection of US citizens, but that their names typically remain concealed or "masked".
Himes said earlier that Trump and his supporters are waging a campaign of deception designed to remove the focus from Russia's actions in the election.
"When your castle is constructed on utter falsehood, one of the things you have to do over time is take all of the power out of the truth," Himes said on CNN's "New Day" Tuesday about the new focus on Rice. "That's a huge win for a White House that wants to both distract the attention of the American people but also for whom doing away with an absolute sense of truth with any power to it is really important."