Washington (CNN) Rep. Adam Schiff, the top Democrat on the House intelligence committee, said Sunday he is treating an immunity request from ex-national security adviser Michael Flynn with "healthy skepticism."

Schiff's indication on CNN's "State of the Union" with Jake Tapper that he might oppose an immunity deal for the former adviser to President Donald Trump's campaign in exchange for testimony related to the committee's investigation into Russian interference in the US election came days after Flynn's lawyer said his client "has a story to tell" but wanted "assurances against unfair prosecution."

Schiff said he'd need to consult with the Justice Department and assess whether Flynn would actually "add value" to the investigation.

"I think we start out with a very healthy skepticism," Schiff said. "We don't want to do anything that will interfere in any case that the Justice Department may decide to bring."

House and Senate committees and the FBI are investigating allegations that the Trump campaign colluded with Russians known to US intelligence to influence the US election. As part of its probe, the House panel is also looking into Trump's accusations that President Barack Obama wiretapped phones in Trump Tower during the campaign.

The White House has provided no evidence publicly to back this claim, and both FBI Director James Comey and National Security Agency Director Mike Rogers told the House intelligence committee last month that they saw no evidence of wiretapping.

Flynn resigned as national security adviser after it became public that he misled Vice President Mike Pence about his conversations with Russia's ambassador to the United States, Sergey Kislyak.

Schiff also noted Sunday that Flynn did not initially disclose payments from Russian entities for speeches he gave in financial disclosures released this weekend and said the committee had requested security documents Flynn submitted before becoming national security adviser to see if he disclosed his financial connections to foreign entities.

The California Democrat also accused President Donald Trump and the White House of attempting to distract from the investigation into allegations of collusion between the Trump campaign and Russian operatives to influence the presidential election. He warned people to look towards Trump's statements, which he said were not "subtle."

"Whenever they see the President use the word 'fake,' it ought to set off alarm bells," Schiff said.

Schiff went to the White House on Friday to look at documents Rep. Devin Nunes, the House intelligence committee chairman, viewed on White House grounds in mid-March that Nunes said pointed to the possible improper unmasking of Trump transition officials in the course of the Russia probe; Schiff said after viewing them that he disagreed with that conclusion. The California Democrat also implied the White House's own presentation to him made him believe the White House might be trying to use the documents to bolster Trump's wiretapping allegations and distract attention from the Russia investigations.

Nunes, R-California, has said he didn't believe the President nor any of his West Wing team were aware he went to the White House grounds to view the documents, and the White House said Monday it learned of Nunes' visit through media reports and directed any questions to the congressman.

But CNN reported last week that two White House aides helped provide Nunes with the documents.

"How does the White House know that these are the same materials that were shown to the chairman if the White House wasn't aware what the chairman was being shown?" Schiff asked. "If these were produced either for or by the White House, then why all the subterfuge?"

In an interview on ABC's "This Week," Republican Sen. John McCain said Nunes had "killed" the bipartisan cooperation needed for the House to have a successful investigation and pointed to the Senate intelligence committee as a hopeful example of a productive, bipartisan dynamic.

Nunes has refused to discuss his sources, and House Speaker Paul Ryan said in an interview Wednesday that while he had not viewed the materials and did not know the source, Nunes told him it was a "whistleblower type." Schiff, however, said he viewed Nunes' involvement as simply a way to cloak the White House's role.

"It certainly is an attempt to distract and to hide the origin of the materials, to hide the White House hand," Schiff said.

Schiff has called for Nunes to step down from his role leading the committee's investigation into alleged Russian involvement in the 2016 election. Former Trump campaign aides and Russian officials have denied any such involvement.