Washington (CNN) The White House is working behind the scenes to limit the testimony to congressional investigations into Russian meddling in the 2016 election, according to multiple sources.

The attempts to curtail testimony to congressional investigators became clear this week when former White House chief strategist Steve Bannon appeared before the House Intelligence Committee and infuriated both sides of the aisle by refusing to answer questions about his work during the presidential transition and in the White House.

At some points during Bannon's six hours of closed-door testimony, his attorney took breaks to confer via telephone with the White House counsel's office to clarify what questions could be answered and came back with the same guidance: Bannon could not discuss any activities related to the transition or his tenure in the White House.

"All shots were called by the White House," says one source familiar with the proceedings.

Publicly, White House officials and President Donald Trump's personal lawyers have touted the administration's willingness to cooperate with the ongoing probes.

"We've been fully cooperative with the ongoing investigations, and we're going to continue to do so," White House press secretary Sarah Sanders told reporters in Wednesday's press briefing. "We encourage the committees to work with us to find the appropriate accommodation in order to ensure Congress obtains all the information that they're looking for."

But when it comes to the congressional investigations, the White House counsel's office is instructing some witnesses to limit their testimony, testing the extent of executive privilege by refusing to discuss any activity that occurred after the 2016 election.

The White House claims that while Congress is entitled to ask any question it wants, privilege can be waived only by the President. They argue that, in this case, the transition is covered by privilege, while the campaign is not.

Democrats see it as an effort to muzzle important witnesses. "This was effectively a gag order by the White House preventing this witness from answering almost any question concerning his time in the transition or the administration. And then any questions even after he left the administration," said California Rep. Adam Schiff, the top Democrat on the committee.

Bannon's team negotiated ground rules with the White House counsel's office the week prior to his appearance before the House Intelligence Committee, according to a source familiar with the situation.

The President's personal legal team was aware of discussions between the White House counsel's office and Bannon's lawyer about protecting a possible privilege claim. But it wasn't their decision, according to a person familiar with the discussions. The protection of the privilege is a matter for the White House, not the President's legal team, because it relates to the office.

Before the hearing, Bannon's lawyer informed a staff member of Rep. Devin Nunes, the California Republican who chairs the House Intelligence Committee, that Bannon planned to claim executive privilege on topics beyond the presidential campaign, a source said.

But that information was apparently tightly held. "It caught me personally by surprise" that Bannon asserted executive privilege, said Rep. Mike Conaway, the Texas Republican leading the committee's Russia investigation.

South Carolina Rep. Trey Gowdy and Florida Rep. Tom Rooney, the other two Republicans leading the Russia probe along with Conaway, also said they weren't aware of any agreement between the White House and committee staff about the scope of Bannon's testimony.

Gowdy added that, if there were an agreement, he didn't think the staff would have told him anyway because he wouldn't have abided by it.

"They wouldn't do that because I'd ask what I think is relevant to ask, and if you've got a legal privilege you can assert it," Gowdy said, adding that Bannon was in a "legally indefensible position."

As it became clear on Tuesday that Bannon was refusing to answer questions, the committee served him with a subpoena to compel him to divulge additional information.

The President's personal lawyers were not consulted on the specific questions that prompted calls to the White House, a source said.

On Wednesday, the White House insisted such coordination between the White House counsel's office and congressional witnesses isn't unusual in a case like this.

"That's the same process that is typically followed," Sanders said. "Sometimes, they actually have a White House attorney present in the room. This time, it was something that was relayed via phone and, again, was following standard procedure for an instance like this, and something that will likely happen again on any other number of occasions, not just within this administration, but future administrations."

But the scope of what Bannon was claiming was privileged shocked members from both parties.

"His version of executive privilege is it covers the transition, the time he was at the White House and covers time forever," Gowdy told Fox News Wednesday. "That is no one's definition of executive privilege."

"I certainly have never heard of an example where executive privilege is claimed for a president-elect, I have never heard of privilege being claimed for conversations between two people that don't include the president, which were precluded from being asked about today," Rep. Jim Himes, a Connecticut Democrat and a member of the committee, told CNN's Anderson Cooper Tuesday.

Lawmakers were also offended that Bannon had already divulged details about some of his post-campaign activities in Michael Wolff's explosive book "Fire and Fury," but then refused to discuss those events with the committee. Bannon's attorney also informed members that he would, in fact, answer those questions when he meets with special counsel Robert Mueller's team because executive privilege doesn't apply to Mueller's investigation.

Sanders declined to say Wednesday whether the White House has actually invoked executive privilege yet or is simply protecting its right to do so in the future.

"I can tell you that this White House is following the same practice that many White Houses before us have, that have gone back decades, that there is a process that you go through: Anytime you have congressional inquiries touching upon the White House, the Congress should consult with the White House prior to obtaining confidential material," Sanders said. "This is part of a judicial-recognized process."

When Attorney General Jeff Sessions appeared before the House Intelligence Committee, in order to preserve the right for Trump to invoke privilege, he refused to answer questions about whether Trump instructed him to hinder the Russia investigation.

National Security Agency Director Mike Rogers and Director of National Intelligence Dan Coats both refused in a public Senate Intelligence Committee hearing to discuss private conversations with Trump and whether he tried to interfere with the FBI investigation into former national security adviser Michael Flynn.

In December, Donald Trump Jr. refused to tell House investigators what he discussed with his father after reports surfaced about the June 2016 meeting Trump Jr. held with Russians in Trump Tower. In this instance, Trump's son cited attorney-client privilege because attorneys were present during the conversation with his father, pushing the issue even further into far murkier legal territory.

Democrats charge that Bannon's appearance before the House committee marks the broadest attempt so far at using privilege to shield events that occurred from the moment Trump was elected.

So far lawmakers have taken only limited steps to challenge witnesses about whether their claims of privilege are legitimate.

Republicans haven't ruled out the possibility of holding Bannon in contempt, but at least one GOP member -- Gowdy -- suggested it was unlikely.

House Speaker Paul Ryan downplayed the issue of whether witnesses like Bannon might be abusing the bounds of executive privilege.

"There has always been a tension on executive privilege between the legislative branch and the executive branch. This goes back to every administration," Ryan said. "Obama exercised executive privilege, Bush did, Clinton did. That is a typical tension that you are going to have between the two branches of government."

Still, Bannon's stonewalling sparked a sharp warning from Conaway -- the Republican leading the House Russia probe -- to White House aides who might follow the Bannon model: "We're going to insist on getting questions we need to answer our report."

Bannon could appear before the House committee again on Thursday and "we fully anticipate" he will answer questions, Conaway said.

For its part, the White House offered a dismissive response to the ongoing Russia probes.

"I think we've been dealing with this hoax for the better part of a year," Sanders said Wednesday. "If we have to endure the ridiculousness for another month, we can certainly handle it."