Jeanine Pirro, the U.S. attorney in Washington, signaled on Sunday that federal prosecutors were still interested in investigating Jerome H. Powell, the Federal Reserve chair who had faced a criminal inquiry regarding a renovation of the Fed’s headquarters amid President Trump’s demands that the central bank lower interest rates.

Ms. Pirro dropped the case last month after a Republican senator with a crucial vote to confirming Mr. Trump’s nominee to replace Mr. Powell, Kevin M. Warsh, said he would hold up that process until prosecutors stopped their inquiry into Mr. Powell. But on Sunday, Ms. Pirro indicated that she could again pursue the case if a continuing internal audit were to find any indication of malfeasance by Mr. Powell.

“We continue to litigate the issue,” Ms. Pirro said on CNN’s “State of the Union,” vowing again that she would also appeal a federal judge’s order from March that had quashed grand jury subpoenas in the case, a major roadblock for the prosecution.

Ms. Pirro’s unwillingness to move on from Mr. Powell’s case despite scant evidence of wrongdoing hinted that the pause on the inquiry could be temporary.

The Republican senator, Thom Tillis of North Carolina, said on Sunday that the Justice Department should not reopen the case into Mr. Powell unless the agency came forward with new evidence of wrongdoing.

“At the end of the day, there was no crime committed, and prosecutors that I’ve spoken with all agree,” Mr. Tillis said on CNN.

The Justice Department opened the investigation into Mr. Powell in an escalation of Mr. Trump’s pressure campaign against the chairman, whom he has continually attacked for resisting his demands to slash interest rates. The inquiry focused on whether Mr. Powell had lied to Congress regarding a $2.5 billion renovation of the Federal Reserve headquarters.

That investigation hit a major roadblock in March when James E. Boasberg, the chief judge in Federal District Court in Washington, blocked prosecutors’ grand jury subpoenas seeking information on the renovations and Mr. Powell’s testimony to Congress. Judge Boasberg described the subpoenas as an attempt “to harass and pressure Powell either to yield to the president or to resign and make way for a Fed chair who will.”

Mr. Powell’s term as Fed chair ends on May 15, but he vowed last week to stay on as a governor who holds a vote on interest rates. He has emphasized that the efforts by Mr. Trump and his allies to exert political pressure on the central bank have motivated him to stay on, despite his earlier plans for retirement.

Mr. Powell can technically remain a governor until 2028. He would be the first Federal Reserve chair to stay on as a governor after an expired term since 1948.

Treasury Secretary Scott Bessent criticized Mr. Powell’s decision to stay on at the Federal Reserve on Sunday, saying that his continued service “violates all norms” and expressing the administration’s wishes that Mr. Powell depart soon.

“It would be inappropriate to overshadow,” Mr. Bessent said on Fox News’s “Sunday Morning Futures.” “I am optimistic that after a period he may move on.”

If Mr. Powell were to leave, Mr. Trump could appoint another governor who might be more amenable to his wishes.

Mr. Trump has tried to fire another Federal Reserve governor, Lisa D. Cook, over dubious allegations of mortgage fraud. The Supreme Court has yet to rule on whether the president can fire Ms. Cook over such claims of wrongdoing, but the justices expressed concern about the implications for the Fed’s independence if her firing were to stand.

Megan Mineiro contributed reporting.