Committee members declined to provide in-depth details on the investigation.
"We have a document that we've signed and we'll be giving out obviously, some announcement at some point," House Intelligence Committee Chairman Devin Nunes told CNN when asked if the members had agreed on the terms of their investigation.
Nunes, a California Republican, added that members have already been briefed on the transcripts of calls between former national security adviser Michael Flynn and the Russian ambassador and are proceeding deliberately on the investigation.
"I'd like for it to go as quick as possible, but at the same time, we're going to try and get all the information that we can," Nunes told CNN as he left a meeting of the House committee. "We'll be looking at anyone and everyone, as I said today, but without any real credible evidence, we're not going to be bringing Americans into there to be interviewed."
Nunes also brushed off calls by Democrats and at least one Republican, Rep. Darrell Issa, for an independent investigation into Russia's influence and hit back against allegations that he coordinated a response to previous reports with the White House.
"They can say whatever they want, but at the end of the day, I hold the gavel, they're in the minority and we're going to do what we want to do. We have the votes and we've been elected to do that. If that ever changes, then obviously that would be different," Nunes told CNN. "At this point, I'm not going to give up jurisdiction of this committee that for a long time that has been trusted with the nation's top secrets. We are not going to give up that jurisdiction to anyone else as long as I'm here."
Tensions escalated Monday between Nunes and the top Democrat working on the Russia investigation, Rep. Adam Schiff, after Nunes said he had seen no evidence yet of Russian officials communicating with Trump campaign aides and Schiff said it was too early to tell.
Schiff later told CNN's Erin Burnett that if high-ranking intelligence officials have been communicating with the White House about the investigation, it "threatens the integrity of the organizations and I think they ought to call a halt to that."
"If we are going to do this in a thorough and objective and nonpartisan way, we need to follow the facts where they lead and not begin with the conclusion the White House would like us to," Schiff said on "OutFront."
'Have not seen any evidence'
High-level advisers close to then-presidential nominee Trump were in constant communication during the campaign with Russians known to US intelligence, multiple current and former intelligence, law enforcement and administration officials told CNN earlier this month
Nunes said he was asked by the White House to call a reporter after The New York Times first reported on contacts
between the Trump campaign and Russians, but he downplayed the request.
"We still have not seen any evidence that anyone from the Trump campaign, or any other campaign for that matter, has communicated with the Russian government," Nunes said on Capitol Hill earlier Monday.
"There is no evidence that I've been presented of regular contact with anybody within the Trump campaign. The only one that's obvious is Gen. (Michael) Flynn's discussions with the Russians, which I would still contend that he was doing what he was supposed to do, which was prepare the President-elect for office by getting as many leaders in front of him as possible," he said.
Trump has personally intensified his attacks on the press as the steady stream of articles about Russian ties to his campaign have emerged. Behind the scenes, White House officials sought help from the men overseeing two of the congressional investigations: Nunes and Senate Intelligence Committee Chairman Richard Burr, according to a recent Washington Post report
But Nunes beat back reports that he was enlisted by the White House to refute the Times reporting, saying: "That didn't happen."
Democrats, however, have latched onto the report. Senate Democratic Leader Chuck Schumer said Monday he was putting Burr "on notice, because what he did was wrong and this is not the way to conduct a fair, impartial investigation."
And Sen. Susan Collins, a moderate Republican and member of the Senate Intelligence Committee said, "I think all of us have to be careful to not create a perception that the White House has any role in this investigation."
Nunes reiterated that he wants to uncover who leaked transcripts of Flynn's calls with the Russian ambassador, which ultimately led to Flynn's resignation as national security adviser.
"We're very interested in figuring out who those people were because they have questions to answer as to what laws did they use to decide to unmask Gen. Flynn," Nunes said.
Schiff said he agreed to investigate the leaks but did not want that to be the main focus of the committee's work.