House Intelligence Committee chairman Devin Nunes is now himself under investigation by the House Ethics Committee.
The panel is looking into claims that the Republican disclosed classified intelligence.
Mr Nunes called the charges "entirely false" and "politically motivated".
He said his decision to step aside came after "several left-wing activist groups have filed accusations against me with the Office of Congressional Ethics".
Mr Nunes added he would continue to fulfil his other responsibilities as chairman, requesting to speak to the ethics panel "in order to expedite the dismissal of these false claims".
Democrats have criticised Mr Nunes for his handling of the inquiry, which is also looking at possible links between the Trump campaign and Moscow.
The House Ethics Committee said in a statement on Thursday: "The Committee is aware of public allegations that Representative Devin Nunes may have made unauthorised disclosures of classified information, in violation of House rules, laws, regulations, or other standards of conduct."
Watchdog groups Democracy 21 and Citizens for Responsibility and Ethics in Washington had asked the House ethics panel to investigate Mr Nunes.
His political foes have accused him of helping the White House to divert attention from several investigations into links between the Trump team and Russian officials.
Mr Nunes has acknowledged making an after-dark trip to the White House grounds last month that even the congressman's own aides were apparently unaware of.
The next day at a hastily arranged news conference he announced he had learned that post-election communications of Mr Trump's team had been monitored by US intelligence agencies as they snooped on foreign officials.
He expressed alarm that information about the then-incoming president's aides had been swept up in US intelligence reports.
Mr Nunes' Democratic colleagues on the panel were furious that he had not shared such information with them before going public.
In the face of much scepticism, Mr Nunes maintains White House officials were not his original source for the claims.
Democrats questioned whether the investigation into Russia's alleged role in the election could proceed objectively.
It's never a good sign when the investigator becomes a bigger story than the investigation.
Such was the case with Congressman Devin Nunes, with his shifting explanations for where and how he acquired sensitive intelligence documents, his decision to keep details from his fellow intelligence committee members, his apparent behind-the-scenes co-ordination with White House sources and his penchant for dramatic press conferences.
All this made him a liability for Republican congressional leadership and the White House. Now he is, at least temporarily, out of the picture.
He may blame an ethics complaint filed by "leftwing activist groups" for forcing the move, but there's little doubt that many Republicans are breathing a sigh of relief. Mr Nunes, at times, seemed out of his depth on the big political stage.
The committee's investigations effectively had been ground to a halt by partisan bickering, and this move is a first step toward rebooting the efforts.
It may be too late, however, as the concurrent Senate intelligence committee investigation has launched more smoothly and with a greater show of bipartisan co-operation.
Members of the House of Representatives often complain of being viewed as the "baby brother" to the upper chamber. The dual Russia probes haven't done much to dispel that notion.
House Speaker Paul Ryan said he fully supported Mr Nunes' decision.
Mr Ryan said he trusts Mr Nunes, but the ehtics inquiry "would be a distraction" for the House Intelligence Committee investigation.
Representative Adam Schiff, a ranking Democrat on the House Intelligence Committee, said he respected Mr Nunes' decision.
"We have a fresh opportunity to move forward in the unified and nonpartisan way that an investigation of this seriousness demands," he added.
A White House spokesman said in response to the announcement: "This is an internal matter for the House".
Texas Representative Mike Conaway will take over that inquiry with the help of fellow Republicans Trey Gowdy and Tom Rooney.
"We're going to proceed with the investigation and follow every lead to its logical conclusion," Mr Conaway said on Thursday.
It is unclear whether Mr Nunes' departure will end the partisan bickering that has brought the committee's investigation to a virtual halt.
But a separate Senate Intelligence Committee probe into Russia's alleged role in the US election appeared to be moving forward, conducting its first round of hearings on the issue last week.
Meanwhile, the FBI also recently acknowledged it is running its own probe into claims of Kremlin political meddling.
Mr Nunes said he plans to return to the House investigation, but he did not provide a timeline.
The head of a key US congressional investigation into alleged Russian hacking has temporarily stepped down amid an ethics inquiry into him.