Story highlights Devin Nunes is the chairman of the House intelligence committee

Despite stepping aside, that means Nunes still can issue subpoenas

(CNN) Rep. Devin Nunes, who stepped aside from leading the House intelligence committee's Russia probe under a cloud of controversy, still is in charge of a key decision: Whether to issue subpoenas to obtain records and testimony central to the investigation.

In a private meeting this week, House intelligence committee members discussed their plans to move ahead with the Russia investigation into meddling in the US election. And the GOP members made clear that the current rules of the committee still apply: That Nunes can issue the subpoenas "upon consultation with" ranking Democrat Adam Schiff or by a vote of the full committee, according to several sources familiar with the matter.

The decision means Nunes still has significant sway to influence the direction of the probe, despite announcing in April that he would still remain chairman of the committee but temporarily step aside from leading the investigation as the House Ethics Committee planned to investigate him for potentially disclosing classified information. Rep. Mike Conaway, a Texas Republican, took his place.

The House panel's approach differs markedly from the Senate Intelligence Committee, which is also investigating the possibility of collusion between Trump associates and Russian officials during last year's elections. On Thursday, members of the Senate committee gave their GOP chairman, Richard Burr, and Democratic ranking member, Mark Warner, blanket authority to issue subpoenas as they see fit. The move was intended to speed up a probe that some Senate Democrats had sharply criticized for moving too slowly.

But this week, members on the House Intelligence Committee were informed that the current standing rules of the committee still apply for issuing subpoenas, sources said, prompting grumbling among some Democratic members who have had more optimism in the leadership of GOP Rep. Mike Conaway of Texas, who is now leading the Russia probe. Nunes' continued power over subpoenas has spurred some tension with Conaway, a committee source said.