"Based upon everything I've seen, the case is solved. And if it were me, I would wrap this case up and move on," he added.
Cummings, a Maryland Democrat, said he would release a full transcript of the committee's interviews with IRS officials by the end of this week, if the panel's Republican chairman, Representative Darrell Issa, does not.
Issa has released his own excerpts of interviews with IRS employees the committee is conducting jointly, which the Republican says suggests the added attention given to Tea Party groups originated from Washington, D.C. and had political motivations.
Issa vowed to press ahead with the investigation and said the IRS manager's comments "did not provide anything enlightening or contradict other witness accounts."
"I strongly disagree with ... Cummings' assertion that we know everything we need to know about inappropriate targeting of Tea Party groups by the IRS," the California Republican said in a statement released by his office.
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Revelations that the tax agency set aside conservative groups for scrutiny has raised a political furor over the past month, leading President Barack Obama to fire the IRS commissioner. The House oversight panel, several other congressional committees and the FBI have launched investigations.
The Treasury Inspector General for Tax Administration issued a report on the matter last month finding no evidence of involvement beyond IRS officials.
Still, Republicans have raised questions about whether the scrutiny was directed politically at Obama's opponents and have sought evidence of any White House involvement.
The House oversight committee has now completed five lengthy interviews with IRS employees, including four based in the Cincinnati office where applications for tax exempt status are handled.
Cummings said congressional investigators now know what happened based on these interviews.
Cincinnati Sought Advice From Washington
The excerpts of interviews with IRS workers released by Cummings indicate that the IRS manager and an underling first decided to contact Washington, D.C. IRS officials for guidance on the cases from groups aligned with the anti-tax Tea Party movement.
They did so to consolidate them, as they might be precedent-setting for future cases, the manager said, according to the interview transcripts.
(Read More: IRS Official Apologizes for 'Star Trek' Tax Spoof)
It was an unidentified Cincinnati IRS worker who reported to the manager, identified as John Shafer by committee aides, who identified the first Tea Party case. That individual has not been interviewed by the committee yet.
Investigators asked Shafer if he believed the decision to centralize the screening of Tea Party applications was intended to target "the president's political enemies."
"I do not believe that the screening of these cases had anything to do, other than consistency and identifying issues that needed to have further development," the manager answered, according to a transcript released by Cummings.
Asked if he believed the White House was involved, the manager replied: "I have no reason to believe that."
John Shafer could not be reached for comment.
"They wanted to make sure that it was handled in a way whereby when other cases came behind it that were similar, that they would be treated in a consistent way," the lawmaker said.
Another Cincinnati screener who worked for Shafer, Gary Muthert, indicated in committee interviews released in part by Issa last week, that "Washington wanted some cases," to review.
Democratic committee staff said Muthert's involvement came later, after the initial screener and Shafer first sought advice from Washington about the legal aspects of the newly-emerging cases.