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Sen. Chuck Grassley of Iowa, the senior Republican on the Senate Judiciary Committee, also Thursday said it’s his “understanding” that Mr. Werfel has asked Ms. Lerner to resign, but that she refused.

Mr. Grassley said the IRS “owes it to the taxpayers” to resolve the situation quickly.

“The agency needs to move on to fix the conditions that led to the targeting debacle,” he said. “She shouldn’t be in limbo indefinitely on the taxpayers’ dime.”

Rep. Darrell E. Issa, California Republican and chairman of the House Oversight and Government Reform Committee, said Ms. Lerner’s invocation of the Fifth Amendment in refusing to testify before his panel Wednesday is no longer valid and that she remains under subpoena. He said the committee is looking at recalling her for testimony.

• Stephen Dinan contributed to this report.