WASHINGTON (Reuters) - The Republican-led U.S. House of Representatives plans to file a civil suit in federal court in the next several weeks over the Obama administration's refusal to give Congress documents about a failed gun-running probe, House Speaker John Boehner said on Sunday.

The Justice Department said on Friday it would not prosecute Attorney General Eric Holder after he was cited a day earlier by the Republican-led House for contempt of Congress for withholding some documents related to the probe. Holder heads the department.

The fight over the documents revolves around "Operation Fast and Furious," a federal law enforcement program intended to track weapons sold in Arizona that were suspected of being transported to Mexico for use by violent drug cartels.

The House on Thursday also voted to give itself the authority to go to court to get the documents that Republicans accuse the Justice Department of withholding.

"We are also going to file in District Court a civil suit over the issue of executive privilege," Boehner told the CBS program "Face the Nation."

"I would expect that to be coming in the next several weeks, but it needs to happen," Boehner said.

The lawsuit could lead to a prolonged court fight while a judge weighs the House demand against the Obama administration's claim of executive privilege to protect the documents.

In a letter to Boehner on Friday, Deputy Attorney General James Cole said Holder properly withheld the documents under executive privilege, which allows President Barack Obama to keep private documents on internal government discussions.

White House Chief of Staff Jack Lew on Sunday accused the House Republicans of carrying out "a political witch hunt." The timing of the planned lawsuit comes in the run-up to the November 6 election in which Republicans are trying to deny Obama a second term in office.

"What they're looking for now is internal kinds of documents that they know are not appropriate," Lew said on CNN's "State of the Union" program.

"The facts are that this was a bad plan, the Fast and Furious. It is something that started in the Bush administration. The attorney general did not know about it. ... And when the attorney general learned about it, what he did was stop it," Lew added.

The Justice Department initially denied that a program was being run that allowed some guns to "walk" into Mexico - a contention it later retracted, raising Republican suspicions.

Republicans accuse the administration of allowing guns to enter Mexico that were used in at least one case to kill a U.S. official.

Some Republicans have called on Holder to resign over the matter, which he has refused to do.

Thursday's vote - making Holder the first sitting attorney general and presidential Cabinet member to be cited for contempt by the full House - was "really unfortunate," said the top House Democrat, Nancy Pelosi.

"To do so ... after the administration had cooperated in every way with them, there is no way they wanted to resolve it," Pelosi told NBC's "Meet the Press" program.

Boehner vowed to pursue Holder. "The only facts that we've received about this entire Fast and Furious operation came from whistleblowers and others associated with it," Boehner said.

"The American people deserve the truth," added Boehner.