(CNN) The chairman of the House intelligence committee has issued subpoenas to the partners who run Fusion GPS, the research firm that produced the dossier of memos on alleged Russian efforts to aid the Trump campaign, according to sources briefed on the matter.

The subpoenas -- signed by California Republican Rep. Devin Nunes -- were issued Oct. 4, demanding documents and testimony later this month and early November.

Earlier this year, Nunes announced that he was stepping aside from directing the committee's Russia inquiry after he became the subject of an ethics investigation into his handling of classified information. But more recently, he has made clear that he is still playing an influential role, despite announcing that he had delegated authority on the Russia matter to Republican Rep. Mike Conaway of Texas.

A source familiar with the matter told CNN that all Russia-related subpoenas have been approved by Conaway, and Conaway confirmed to CNN Monday he asked for the most recent subpoenas.

But the subpoenas appear to be the latest fight in an investigation that has periodically been hobbled by controversy and infighting.

A Democratic committee source said "the subpoenas were issued unilaterally by the majority, without the minority's agreement and despite good faith engagement thus far by the witnesses on the potential terms for voluntary cooperation."

Indeed, the move blindsided some committee members, multiple sources told CNN. And it has angered some on the committee who say that Nunes is still seeking to direct an investigation he was supposed to have no involvement in leading.

"He's not in any way, shape or form working on the investigation," said one Democratic committee member. "He's sitting outside the investigation and pushing it in a political direction."

Rep. Eric Swalwell, a California Democrat, told CNN's Wolf Blitzer that Nunes appeared to be "trying to undermine the investigation."

"This would violate that recusal if this is indeed what he has done," Swalwell said.

Conaway said the committee's procedures were to consult with the committee's Democratic leader, and that "the mechanics on that fit in with the chairman's responsibilities."

"I'm trying to maintain good relations, but at the end of the day we need to get those records that are subject to those subpoenas," Conaway said.

Asked by CNN Monday why he issued the subpoenas, Nunes declined to comment. "You can ask, but you're not going to get a response," Nunes said.

Previously, in a June interview with CNN, Nunes said: "When I temporarily stepped aside from leading the investigation, that's exactly what it means: It doesn't mean I wasn't going to be involved, it doesn't mean I wasn't going to be fully read in."

Joshua Levy, an attorney for Fusion GPS, said the firm's founder, Glenn Simpson, already provided a 10-hour interview to the Senate judiciary committee and Nunes could first seek to review that testimony.

"This is a blatant attempt to undermine the reporting of the so-called 'dossier,' even as its core conclusion of a broad campaign by the Russian government to influence the outcome of the 2016 presidential election has been confirmed by the US intelligence community and is now widely accepted as fact," Levy said.

"Rep. Nunes recused himself, but now appears to be running a parallel investigation outside of the official (House intelligence) investigation run by Reps. Conaway and (California Rep. Adam) Schiff. His actions undermine the House, its investigation and the public's ability to learn the truth. As we evaluate these subpoenas, we have serious concerns about their legitimacy."

The Fusion GPS subpoenas mark at least the fourth time Nunes has inserted himself into the investigation since his April announcement that he was temporarily stepping aside.

Earlier this summer, Nunes led an effort to subpoena the FBI, CIA and NSA about Trump associates whose identities were allegedly unmasked during the presidential transition by Obama administration officials.

Later, a pair of GOP staffers on the panel flew to London to urge the British agent who wrote the dossier, Christopher Steele, to appear before the committee, an effort several committee members said was led by Nunes. And in late August, Nunes signed off on subpoenas to Attorney General Jeff Sessions and FBI Director Christopher Wray to provide the panel with records about the Justice Department's relationship with Steele and the Trump dossier, warning in a letter that he would haul them to Capitol Hill to answer questions at a public hearing if they did not comply.

Tension has been building on the House intelligence committee over Nunes' role ever since he first secretly traveled to the White House in March to review classified intelligence reports that he said showed rampant misconduct by US officials in revealing the identities of unsuspecting Americans, including Trump officials. Nunes later briefed President Donald Trump on the matter, and seemed to give cover to the President's unsubstantiated allegations that former President Barack Obama had Trump Tower wiretapped during the campaign. Nunes, however, did say that he had seen no evidence that Trump Tower was wiretapped.

After the House ethics committee in April announced it would investigate Nunes over allegations he disclosed classified information, the Republican chairman said he would temporarily step aside from the probe -- a move that satisfied Democrats on the panel at the time.

But while the announcement was widely viewed as a recusal from the Russia investigation, Nunes has said privately and publicly since then that he never recused himself.

In fact, as chairman, Nunes still retains significant power to influence the investigation -- even as Conaway is in charge of leading the investigation.

Most notably, Nunes still has the power to issue subpoenas "in consultation" with Schiff, the committee's top Democrat.

But unlike other committee members, Nunes does not attend classified hearings of the key witnesses in the Russia probe, sources said, and instead appears to be making his push from the outside.

The committee's Democrats face a dilemma: They still need Nunes to sign off on subpoenas that Conaway and Schiff are seeking directly tied to the Russia investigation.

As a result, intelligence committee sources say Democrats are opting not to object loudly to Nunes issuing subpoenas, so long as he continues to sign off on the subpoenas that Conaway and Schiff want to issue as part of their probe.

"His recusal is basically entirely up to his discretion," said one intelligence committee source. "When you talk about the unmasking situation, people don't see that as separate, but they don't really have a way of stopping it."