(CNN) The White House said Thursday that members of its staff had uncovered materials regarding surveillance in the 2016 election, raising questions about whether President Donald Trump's own aides had shared classified information with the top Republican on the House Intelligence Committee in an attempt to bolster Trump's claims he was wiretapped.

In a letter sent Thursday, Trump's top White House lawyer invited the highest-ranking lawmakers on the House and Senate intelligence committees to view classified materials, which it said had been uncovered in the "ordinary course of business."

"Our view was that the smart move was to make all the materials available to the chairman and the ranking member of the relevant committees," Press Secretary Sean Spicer said during the White House briefing Thursday. "We are focused on the substance of it and I think the goal is to make sure people have the substance that are looking into this."

Spicer said the information being made available to lawmakers was uncovered by the National Security Council. In the letter, White House Counsel Don McGhan wrote the material related to whether "information collected on US persons was mishandled and leaked."

That closely maps with how Rep. Devin Nunes described the information he viewed at the White House last week, and subsequently briefed Trump on during a hastily arranged session.

Officials declined to confirm whether the two sets of information are the same. But Democrats cast doubts on the timing, and questioned White House's intentions in making the information available to a broader set of lawmakers.

Rep. Adam Schiff, the top Democrat on the House intelligence panel, said he was invited to the White House to view the intelligence documents, but in a written reply said expressed "profound concern" with the way the materials were being made available to the committee.

The developments came the same hour the New York Times reported that two White House officials played a role in providing Nunes the intelligence he received at the White House last week, a report Spicer would neither confirm nor deny Thursday.

Schiff said he wants to know why the materials appeared to be "laundered" through Nunes if they originated at the White House and expressed "deep concern" in a letter to the White House that the materials were being made the same day the Times story broke.

"If that was designed to hide the origin of the materials, that raises profound questions about just what the White House is doing that need to be answered," Schiff said. "I have asked the White House for their assistance in answering those questions."

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"Why all the cloak and dagger stuff?" Schiff added.

In the letter, Schiff asked White House if the materials he's been invited to view are the same as the intelligence viewed by Nunes last week.

Spicer again declined to name who within the administration helped Nunes gain access to the White House complex, or who provided him with the information.

But he suggested the information being made available to lawmakers related to Trump's wiretapping claims, which the President levied on Twitter earlier this month but which officials have struggled to back up.

"There's a belief that the President has maintained that there was surveillance that occurred during the 2016 election that was improper and that we want people to look into this and to take the legal, responsible steps to both understand it and then address it," Spicer said.

This comes as Schiff and Nunes are trying to get their Russia investigation back on the rails following Nunes' moves last week.

Nunes and Schiff met Thursday after a week's worth of canceled hearings and bickering between the committee leaders, as their investigation turned partisan following a decision by Nunes, a Republican, to go to the press and White House with intelligence before alerting the committee.

"We're doing our best to try and get the investigation back on track," Schiff said following the meeting. "We're in the process of exchanging witness lists and are going to see if by the end of the day we can agree on at least a common set of initial witnesses."

CNN has reached out to Nunes for comment on the meeting and has not yet received a response.

The committee leaders were trying to agree on a common set of initial witnesses, Schiff said, an issue that prompted the cancellation of both an open and closed hearing this week.

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Schiff said he and Nunes have agreed to go forward with a closed hearing with FBI Director James Comey and National Security Agency Director Adm. Mike Rogers. He also requested that Nunes agree to hold the public hearing with former acting Attorney General Sally Yates, former CIA Director John Brennan and former Director of National Intelligence James Clapper, though he said the chairman has yet to commit to do so.

The committee's investigation has effectively ground to a halt after Nunes went to the White House last week with information of potential surveillance of Trump's aides, without telling Democrats on the committee first.

Schiff, House Minority Leader Nancy Pelosi and other top Democrats have called for Nunes to recuse himself from the Russia investigation.

Schiff said Nunes has still not revealed the intelligence he said he shared with Trump and has pledged to share with the committee, or who Nunes met with at the White House.

"It certainly was a part of our discussion, but beyond what we agreed to do, or hope to achieve to do by the end of the day, I really don't want to get into specifics," Schiff said.

The California Democrat said he had a "great sense of nostalgia" seeing Senate intelligence committee leaders holding a news conference together on Wednesday, saying that he had that relationship with Nunes up until last week.

But Schiff argued it was up to Nunes to restore credibility in the committee's investigation.

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"Ultimately the speaker and the chair decide who they want to run this investigation and they'll have to articulate why and how they feel that can be done credibly," Schiff said. "But our job is to do everything in our power to be responsible to go forward and be constructive and that's what we're doing."

The Senate intelligence committee has a list of 20 witnesses it's called, and Schiff said he thinks the House panel is looking at a similar number.

That includes Paul Manafort and Jared Kushner, Schiff added.

"I think that we certainly had agreement today that the witnesses that we feel are appropriate, they won't stand in our way, and we feel the same way about witnesses they want to call," he said. "So I think that was an encouraging sign."

A Senate intelligence committee source said members view Nunes' claims as a "sideshow" and feel no urgency to run to the White House to view the documents.