A federal judge said the IRS isn’t to be trusted as he and his colleagues tried Thursday to figure out whether the tax agency is still targeting tea party groups for intrusive and illegal scrutiny.

Judge David B. Sentelle of the U.S. Court of Appeals for the D.C. Circuit said there is strong evidence that the IRS violated the constitutional rights of the groups when it delayed their nonprofit status applications and asked inappropriate questions about their political beliefs.

The agency’s insistence that it has retrained employees and instructed managers to behave better did not mollify the judges, who said past IRS behavior doesn’t lend itself to the benefit of the doubt.

PHOTOS: Best states for concealed carry — ranked worst to first

“It’s hard to find the IRS to be an agency we can trust,” Judge Sentelle said.

On Capitol Hill, a group of conservative House Republicans called for IRS Commissioner John Koskinen to be impeached. They delivered a series of speeches on the chamber floor saying the man brought in to clean up the agency has failed.

House Speaker Paul D. Ryan, Wisconsin Republican, didn’t go as far as calling for impeachment, but he did say “the IRS is not being led well.”

PHOTOS: See Obama's biggest White House fails

The agency’s myriad problems include ignoring many taxpayers’ calls and succumbing last year to a massive computer hack in which hundreds of thousands of taxpayers’ most sensitive information was stolen from IRS computers.

The agency continues to grapple with fallout from the tea party targeting. An inspector general said hundreds of groups’ applications for nonprofit status derailed while the IRS put them through intense scrutiny.

Some groups dropped out rather than face the inquiry, while others battled. At least two groups have been awaiting a decision for more than five years.

IRS officials acknowledged they erred but said the problem was bad training and confusion about a 2010 Supreme Court decision, not an intent to target groups for political purposes. The agency says it tried to follow all nine of the inspector general’s regulations for cleaning up its act.

“IRS responded enthusiastically,” said Judith A. Hagley, the Justice Department lawyer representing the IRS.

The judges Thursday were not convinced.

“How much has really changed?” said Judge Douglas H. Ginsburg.

A lower-court judge sided with the IRS, saying that since most groups were approved, the targeting has stopped. That judge tossed the cases, saying they were now moot.

But the tea party groups pointed to a report last year by the Government Accountability Office that said conservative nonprofit groups were still more likely to face follow-up audits from the IRS, evidence that political targeting was continuing.

Ms. Hagley acknowledged “potential problems” but said those were later in the process — not in the initial stage that the tea party groups were challenging.

The IRS is also holding on to answers to the intrusive questions it asked of tea party groups and said it is required by law to make that information available to the public.

Ms. Hagley said the groups were specifically warned. If they didn’t want the information released, she said, they should have refused to answer the questions and sued if the agency didn’t approve them.

But John Eastman, an attorney for True the Vote, one of the groups challenging the IRS in court, said the tax agency suggested that not answering the questions would lead to dismissing the application without a ruling one way or another. No ruling means no chance to sue, Mr. Eastman said.

He asked the appeals court judges to order the IRS to expunge all of the answers it coerced from the tea party groups. He also said the IRS should take the groups off the special audit list and that the rest of the case should be sent back to a lower court so more facts could be gathered.

The tea party groups are also trying to pursue a case against former IRS executive Lois G. Lerner and other staffers involved with processing the applications, accusing them of violating the groups’ constitutional rights.