Recent comments from prominent House Republicans suggest that funding for the FBI could become a central debate when the House needs to pass a new budget in September, as the House Judiciary Committee chairman, Congressman Jim Jordan, is amping up his crusade to defund the FBI.

On Fox News’s “Sunday Morning Futures,” Mr. Jordan said that cutting funding was one of his priorities and that it should be a priority for the House GOP conference as a whole.

“So we have to use the appropriations,” Mr. Jordan said. “So we have to exercise our authority, the power of the purse, to limit what the federal government, what the FBI and justice department, are doing to the American people.”

According to Mr. Jordan, House Republicans plan to target the FBI’s funding in the appropriations bills that the House must pass to fund the government. He said they plan to pass these bills to fund the government on a month-to-month basis.

Mr. Jordan’s promise follows testimony from an FBI whistleblower and Special Counsel John Durham’s report on the FBI’s investigation into President Trump’s 2016 campaign., which criticized the FBI for anti-conservative bias.

Mr. Jordan’s threats to defund the FBI represents an escalation of what has become a campaign from leading voices in the Republican Party.

Representative Marjorie Taylor Greene, for one, has said that she won’t vote for a budget unless it includes slashing funding for the Department of Justice and the FBI. President Trump has called on Republicans to decrease funding for federal law enforcement as well.

Mr. Jordan also hinted at a new congressional investigation into Secretary Clinton’s global initiative and the Clinton Foundation.

“They not only didn’t investigate her like they did President Trump,” Mr. Jordan said. “We’re going to talk with our lawyers. We’re going to talk with Speaker McCarthy with where we proceed from here.”

Mr. Jordan’s railing against federal law enforcement comes in the wake of Durham report. So far, though, House Republicans have not proposed legislation to remedy what they claim are problems with the FBI and other federal law enforcement agencies.

Inside the Republican conference, members are not uniformly in favor of gutting law enforcement agencies, slashing their budgets, or even, it seems, broad changes.

Representative Ken Buck has expressed reservations in endorsing the call to slash law enforcement budgets coming from members like Mr. Jordan and Ms. Greene, telling CNN: “I will not support any drastic cut in appropriations.”

Other Republicans, like Congressman Chip Roy, have said they would like to refocus the FBI and limit it to a role similar to what it played more than 20 years ago.

“I would like to take it back at a minimum to pre-9/11 to focus on crime and working with local and state jurisdictions to combat crime and not be so much dwelling on the domestic terrorism bit, which they exploited in ways that I don’t think is particularly beneficial,” Mr. Roy told CNN.

Even Mr. Roy’s more balanced push for changes, though, has caveats. For one, he called on federal agencies to selectively enforce the law and endorsed the idea of restricting funding for agencies that enforce the FACE Act, which protects individuals seeking abortions as well as some religious freedoms.