Rep. Trey Gowdy (R-S.C.) asks questions as former Homeland Security secretary Jeh Johnson testifies about Russian meddling in the 2016 election before the House Intelligence Committee on Capitol Hill on Wednesday. (Aaron P. Bernstein/Reuters)

The new chairman of the House’s most powerful investigative committee said Friday that, with limited exceptions, his panel will not probe matters related to the alleged Russian interference in the presidential campaign — including President Trump’s possible obstruction of the federal investigation into it.

Rep. Trey Gowdy (R-S.C.), who was named chairman of the House Oversight and Government Reform Committee last week, told reporters that the investigation is more squarely under the purview of special counsel Robert S. Mueller III and other congressional committees.

“I told Bob Mueller Tuesday that I would never do anything wittingly or unwittingly that veered over into his lane, and his lane is broad, and it is undetermined at this point,” he said.

Gowdy referred to the Justice Department order appointing Mueller that authorized him to probe “any matters that arose or may arise directly from the investigation” into Russian election interference. “That’s pretty broad,” he said.

The decision to defer to other entities stands to vex Democrats who watched Gowdy and his predecessor, outgoing Rep. Jason Chaffetz (R-Utah), vigorously pursue what they considered to be politically motivated probes into Democratic presidential nominee Hillary Clinton even as Justice Department and other committees probed the same matters.

Gowdy said keeping clear of Mueller was a bipartisan sentiment: “I don’t think you are going to see many Republicans or Democrats wanting to get into that lane until the special counsel has completed his investigation.”

But Rep. Elijah E. Cummings (Md.), the ranking Democrat on the committee, noted in a statement that the Justice Department has acknowledged the necessity of congressional oversight and said lawmakers “do not have the right to remain silent.”

“It is a known fact that interference in our election will happen again if we do not take serious steps to prevent it,” he said. “The voters did not send us here to sit on the sidelines while our government is getting attacked. Chairman Gowdy is a very talented lawyer, and I believe he and I can work together to investigate this and make reforms to prevent it from happening again.”

Gowdy said there were Trump-related matters that he did see falling within the Oversight panel’s purview — procedures for issuance of security clearances, for instance, and the constitutional prohibition on accepting “emoluments” from foreign benefactors.

But Gowdy said, for instance, he was not interested in seeking memos written by former FBI director James B. Comey detailing his interactions with Trump before he was fired. Chaffetz had requested the memos, but the FBI declined to provide them, citing Mueller’s probe.

“Judiciary, for sure, would be, I think, the proper committee to provide oversight over the Department of Justice and the FBI,” he said.

A former state and federal prosecutor who also holds seats on the House Intelligence and Judiciary committees, Gowdy said he wished to “respect jurisdictional integrity” as chairman and keep his panel focused on matters squarely reserved to it under House rules — such as the coming 2020 Census and the D.C. government.

But the panel also possesses broad “permissive” jurisdiction to probe virtually any matter involving the executive branch of government. Gowdy said he would not hesitate to investigate the Trump administration — when warranted.

“The legislative branch should do what it’s supposed to do, and it should not be usurped and it also should not abdicate its responsibilities,” he said. “The executive branch under President Obama was resistant of that, and we had to get to court to get some of that, and I expect the executive branch under President Trump to be resistant, so that’s just a natural tension.”

While the Oversight panel is known for its pageantry — and grandstanding — at its open hearings, Gowdy said his preference was to use hearings to present findings gathered after the panel does its investigations.

“If I were to devise an inefficient way to gather facts, I don’t know that I could devise anything better than five-minute increments alternating between [Republicans and Democrats],” he said.

Democrats are pressing Gowdy to use his powers more aggressively, much as his predecessors used their power to investigate alleged Obama administration abuses in the Justice Department, Internal Revenue Service and elsewhere.

On Wednesday, Oversight Committee Democrats asked White House Chief of Staff Reince Priebus for documents concerning the decision to allow Michael Flynn, Trump’s former national security adviser, and Jared Kushner, Trump’s son-in-law and senior adviser, to maintain security clearances following allegations that they failed to disclose foreign contacts during the initial application process.

No Republicans joined the letter, and Gowdy said Friday that he did not see the matter as being a matter for the committee.

“We do have a role in the process, and we can certainly weigh in on whether it needs to be tightened up,” he said. “But the specifics of individuals who are alleged to have committed criminal acts in the application of security clearances — we don’t investigate crime.”

With regard to the emoluments question, Gowdy said he was primarily interested in plumbing the legal implications of the constitutional clause, which maintains that federal officials must not “accept of any present, Emolument, Office, or Title, of any kind whatever, from any King, Prince, or foreign State.”

“The first challenge to me is understanding the parameters, how has it historically been applied, and then from that, you can determine whether or not you think there’s been a breach,” he said.

Gowdy suggested he would like to see Rep. Jamie Raskin (D-Md.), a constitutional law professor, and a Republican counterpart on the committee explore the question.

Raskin said Friday that he would be glad to look at the matter but did not want that to substitute for rigorous oversight of Trump’s foreign business entanglements.

“We need to do both,” he said. “Personally, I don’t think that the legal question is that complex.”