Washington (CNN) Lawyers working with a team led by special counsel Robert Mueller approached the Senate intelligence committee this summer with a request: They wanted the transcript of an interview Senate staff had conducted with former Trump campaign chairman Paul Manafort.

But they were blocked. Manafort's lawyers said they had not authorized Mueller's legal team to access the interview transcript under the agreement with the committee, even though Mueller's attorneys said they had been given permission. The matter is still under discussion, sources say.

The previously undisclosed fight, described to CNN by multiple sources, underscores the new challenges as congressional committees and Mueller's operation head into a more intense phase of their parallel -- and sometimes, conflicting -- investigations into Russian election meddling and any collusion with Trump associates.

There are three committees on Capitol Hill competing for information and witnesses -- and there is little, if any, communication among them, even as congressional officials say they all are preparing to intensify the pace of their inquiries this fall. While the Hill investigations into Russia's meddling have been underway since the beginning of the year, the next few months could be the most consequential in terms of hearing from witnesses and gathering documents, sources say.

That could mean early signs of tension between the special counsel and the Hill become more pronounced as the competing congressional inquiries try to determine whether there was any collusion and as Mueller potentially pursues criminal charges.

Top lawmakers on the committees say they have confidence they can avoid conflicts with Mueller's team, but the investigations have different purposes. Mueller's is geared toward prosecuting potential crimes. If no charges result, there's no guarantee the public will find out what Mueller found in his inquiry.

Mueller's team has employed some aggressive tactics. In one such case, Mueller's team may have obtained evidence in the raid of Manafort's home that was not covered by the search warrant, sources told CNN.

Moreover, Mueller's team has kept top lawmakers mostly out of the loop about the developments in its inquiry and has urged Congress to schedule testimony of some key witnesses in public session -- to avoid the possibility that the special counsel may be blocked from accessing information given to the committees privately.

But lawmakers, who take pride in their oversight role, have instead moved forward with private witness interviews, including Donald Trump Jr., who is expected to head to the Senate intelligence committee this month, sources say, and is expected to meet with the Senate judiciary committee as well.

The Senate intelligence panel is considering holding public hearings this fall with some key witnesses, according to a source familiar with the private talks. And, sources said, the committee is now searching for new details around the late Republican operative Peter Smith, who claimed he tried to obtain Clinton emails hacked by the Russians during the last election season.

Across the Capitol, the House intelligence committee now is increasingly focused on the past efforts by Trump associates to move forward on a Trump Tower project in Moscow, sources familiar with the probe told CNN, a matter almost certainly under review by Mueller's team as well.

Plus the House panel is now trying to get its hands on a draft memo that reportedly included President Donald Trump's initial justification in his firing of then-FBI Director James Comey -- a memo that Mueller already has but one that the committee may need to access through the White House rather than the special counsel.

"It's probably past time for our committee to subpoena the White House to make sure we get all relevant documents," California Rep. Adam Schiff, the top Democrat on the House intelligence committee, told CNN.

How multiple inquiries complicate the investigation

On Capitol Hill, the closed-door transcribed interviews are causing complications in the delicate relationship with the special counsel.

After Manafort privately interviewed with Senate intelligence committee staff in late July to discuss the June 2016 meeting between Trump Jr. and Russian operatives, Mueller's lawyers have struggled to get a copy of the interview transcript.

Manafort's attorneys, in talks with the special counsel's office, agreed to allow Mueller's team only to get the documents Manafort had turned over to the committee, not the interview transcript, according to the sources.

Yet an attorney with the Mueller team later told the committee that they were authorized by Manafort's representatives to have the Manafort interview transcript, sources familiar with the discussions told CNN. Committee lawyers later learned from Manafort's attorneys that they had not provided that consent, the sources say.

As a result of the dispute, the committee hasn't turned over any documents and the matter is still under discussion, sources say.

A spokesman for the special counsel declined to comment, as did a Manafort spokesman and the intelligence committee.

Mueller has privately met with leaders of the main three committees investigating the Russian election meddling, in an effort to "deconflict" with Capitol Hill to ensure the two sides are not in conflict when it comes to witnesses.

But sharing information hasn't always been easy. After weeks of demands on Capitol Hill for memos Comey wrote describing his interactions with Trump, including when the President allegedly asked him to drop the FBI investigation into his ex-national security adviser Michael Flynn, top lawmakers eventually got to see it -- with conditions.

The leaders of the Senate judiciary committee, for instance, could read the memos but not take notes or get copies of them, sources said.

The aggressive tactics by Mueller's team extend beyond Capitol Hill. He has put enormous pressure on Manafort -- someone who is also in the crosshairs on the Hill given his past work with a pro-Russian Ukranian political party. Mueller issued subpoenas to Manafort's former lawyer and current spokesman and authorized a pre-dawn raid of his Virginia home in late July.

During that raid, Mueller's investigators took documents considered to be covered by attorney-client privilege, sources told CNN.

Lawyers from the WilmerHale law firm, representing Manafort at the time, warned Mueller's office that their search warrant didn't allow access to attorney materials. The documents in question have now been returned, the sources say.

The episode raised questions about whether investigators have seen materials they weren't entitled to obtain.

"You can't unsee something," one source said.

It's not an uncommon problem in FBI investigations. US attorneys typically have separate document-review teams to prevent investigators from handling materials they aren't allowed to have. It's not clear what procedures Mueller's office uses.

Mueller's spokesman declined to comment.

After meeting with Mueller earlier this summer, Senate Intelligence Chairman Richard Burr said it was not necessary for the committee leaders to meet with Mueller again. "I think we'll be in communication personally with him on any aspects that might bleed over from one to the other," he told CNN

Busy fall on the Hill

Each of the three committees received more than 20,000 pages of documents from the Trump campaign about communications involving Russia, and aides to each of the panels have spent the August recess digging through the documents.

This week, members of each of the committees will be briefed on some of the findings and will discuss new leads they will want to chase, lawmakers said.

One area of intense interest surrounds Trump attorney Michael Cohen and Russian-American businessman Felix Sater -- both of whom are expected to be called to meet with the House intelligence committee and likely the Senate panel as well. In emails provided to Congress, both men discussed efforts to move forward on a Trump Tower project in Moscow and sought to get help from the highest levels of the Kremlin, undercutting the President's repeated claims of not having any business in Russia.

Cohen was scheduled to meet with the House panel this week but has rescheduled his interview, according to people familiar with the matter.

"It's A-level interest," said one source close to the House inquiry, referring to the Trump Tower project in Moscow.

But that's hardly the lone area that lawmakers plan to probe nor the last big-name witness expected to be called in to testify.

Jared Kushner, the President's son-in-law who attended the June 2016 Russia meeting with Trump Jr. and had multiple contacts with Russian officials last year, is expected to be called back to meet with senators after he met with just Senate staff in July, senators said. The Russians who attended the Trump Tower meeting also remain of high interest to the panels.

Roger Stone, the President's longtime friend and adviser whose name has often surfaced as part of the Russia probe, could meet with the House panel as soon as this month, sources said. It's unclear when he'll meet with senators.

And the Senate intelligence committee is pushing to obtain new information about the unusual circumstances surrounding Smith, the veteran GOP operative who told The Wall Street Journal he was on a mission to obtain the hacked Clinton emails. After the stories about his efforts were published this summer, Smith killed himself in a Minnesota hotel room.

Matt Tait, a cybersecurity expert who publicly acknowledged in July being contacted by Smith, is among those the Senate panel is interested in hearing from, sources said.

Tait declined to comment to CNN.

Lawmakers are trying to learn whether that's an area the special counsel is probing as well.