WASHINGTON (CNN) -- Members of the House intelligence committee got back to work Tuesday, setting up the next steps in their investigation, even as opposing forces threaten to pull the sides apart again.

House Intelligence Chairman Devin Nunes said late Monday that investigators had agreed on the list of witnesses they plan to interview. GOP Rep. Peter King suggested Tuesday that 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.

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.

FBI Director James Comey announced in the House's first public hearing that the agency has been investigating possible collusion between top aides on the campaign 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.

The full House intelligence committee is set to discuss the Russia investigation at a meeting Tuesday afternoon -- the latest sign that the investigators are working together again one week after the lead Democrat on the investigation, Rep. Adam 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 unmasking Trump transition aides and called the allegations against her as "absolutely false."

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.

Rep. Jim Himes, a Connecticut Democrat on the House investigation, accused Trump and his supporters of 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."

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