* UN will work to make Nov. 7 run-off poll credible

* Ban denies that UN played down extent of fraud (Adds quotes, details)

By Louis Charbonneau

UNITED NATIONS, Oct 20 (Reuters) - U.N. Secretary-General Ban Ki-moon on Tuesday welcomed Afghan President Hamid Karzai's acceptance of a run-off presidential election but said organizing a second poll would be a "huge challenge."

"I commend President Karzai for the leadership he has displayed and for his commitment to ensuring full respect for Afghanistan's constitution and its democratic processes," Ban told reporters at U.N. headquarters.

Ban said the world body would do everything possible to make the Nov. 7 run-off election in Afghanistan between Karzai and his former foreign minister transparent and credible.

"You can understand there's a huge challenge in conducting a second election," Ban said. "We will try to ensure that all Afghan people should be able to express their own will freely without intimidation or threat."

"We'll do our best ... to make these elections fair and free of fraudulence," he said.

Ban acknowledged that there had been widespread fraud in the Aug. 20 election. He also dismissed criticism that the United Nations had tried to play down the extent of the fraud in the disputed vote.

"We must not repeat what they have done last time," he said about the widespread problems with the vote.

Ban's special envoy to Afghanistan, Norwegian diplomat Kai Eide, appeared with Karzai at a news conference in Kabul, where the Afghan leader announced his decision to accept the ruling of the government-appointed Independent Election Commission.

BAN REJECTS CRITICISM OF U.N. ROLE

The IEC's ruling came after a U.N. election fraud watchdog invalidated tens of thousands of votes for Karzai. That investigation, published on Monday, pushed the vote for Karzai back below the 50 percent level needed to avoid a run-off.

The decision however presents a logistical nightmare, with Afghanistan's harsh winter approaching fast.

Ban was asked if he felt the United Nations had lost credibility because he fired Eide's American former deputy Peter Galbraith, who had complained that Eide had turned a blind eye toward the extent of the fraud in the August vote.

Without responding directly, Ban said Galbraith's proposals would not have improved the outcome of the summer election.

"The idea suggested by Mr. Peter Galbraith was to reduce the number of polling stations to prevent possible fraud," he said. "That was not acceptable."

"Our principle was to open as many polling stations as possible so that as many people (as possible) could participate in their vote," he added. "The question did not arise whether there was fraud or not. We knew that there was fraud. We reported that there was fraud."

Eide has repeatedly denied Galbraith's allegations that he played down the problems with the election, saying the charges were unfair and untrue. (Additional reporting by Michelle Nichols; Editing by Stacey Joyce and Jackie Frank)

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