The FBI is investigating claims that Ahmad Chalabi (search), once pegged by the American-led coalition as the favorite to lead the new Iraqi government, was moonlighting for the Iranians as a spy against the United States.

Fox News has confirmed through U.S. government sources that the FBI is probing an intercepted Iranian message saying that Chalabi had told Tehran officials that the U.S. had broken a secret code used by Iranian spies. Chalabi on Wednesday denied the charge.

FBI agents have begun to question Defense Department officials in an effort to find out who gave information to Chalabi, government sources told Fox. The inquiry is still in its early stages.

"Mr. Chalabi has had a difficult relationship with the government recently, but nothing is forever," National Security Adviser Condoleezza Rice (search) told Fox News Wednesday. "It's not what his relationship is with us, it's what his relationship is with the Iraqi people."

"Chalabi's future in Iraq is up to the Iraqis," she told Fox.

Chalabi is a former Iraqi exile and the founder of the Iraqi National Congress who once was a favorite of the Bush administration.

But in recent weeks, the former coalition darling fell out of favor with the feds after suspicions surfaced that he passed information to Iran that U.S. intelligence had been listening into Iranian intelligence.

According to media reports, Chalabi told an Iranian intelligence official that the United States had gained the ability to monitor secret communications from Iran. Revealing such information would expose one of the United States' most important sources of information about Iran.

In Najaf, Iraq, Chalabi told The Associated Press that the reports he leaked such information to Iran are "false" and "stupid."

"Where would I get this from?" Chalabi asked. "I have no such information. How would I know anything about that? That's stupid from every aspect."

Chalabi and other Shiite Muslim figures are in Najaf to try to shore up a cease-fire between U.S. troops and radical Shiite militiamen.

The Chalabi story was first reported by CBS News on Tuesday. Following the broadcast report, The New York Times, Los Angeles Times and The Washington Post followed with similar stories, all quoting anonymous U.S. intelligence officials.

The New York and Los Angeles papers said they had learned some details of widely reported U.S. assertions last month that Chalabi had given classified material to Iran, but had agreed not to publish those details at the request of U.S. officials who said to do so would endanger an ongoing investigation.

The two papers said those requests to withhold the information they had gathered were withdrawn Tuesday when other news accounts began appearing.

A CIA (search) official declined to comment on the reports Tuesday night.

American officials quoted in the news reports said Chalabi told the Baghdad chief of the Iranian spy service that the United States was reading its communications and that the Iranian spy described the conversation in a message to Tehran, which was intercepted by U.S. intelligence.

The New York Times account said Iranians in Tehran then sent a bogus message to Baghdad purportedly disclosing the location of an important weapons site, in an apparent attempt to test whether what they were hearing from Chalabi was true.

The idea was that if the United States was able to intercept such transmissions, Americans would react by going to the weapons site. They intercepted the message, according to the Times, but did not take the bait by going to the weapons site.

Chalabi reportedly told the Iranian he had he had gotten the information from an American who had been drunk.

FBI agents were reporting to be questioning Defense Department officials in an effort to find out who gave such information to Chalabi.

Chalabi, a member of the Shiite Islamic sect to which the majority of Iranians and Iraqis belong, once was a favorite of Pentagon officials.

He had provided intelligence to the Bush administration about weapons of mass destruction, which was used to justify the U.S. war against Iraq, but his information came under major criticism after no weapons were found.

The CIA has long been suspicious of Chalabi's Iraqi National Congress, but he had maintained strong supporters in other government agencies.

Until last month, his organization was on the U.S. government payroll, receiving roughly $340,000 a month from the Defense Department for intelligence under a specific authorization from Congress.

While refusing to discuss the new intelligence report, Rice did talk in general terms about U.S. ties to Chalabi.

"We had a relationship with Mr. Chalabi and his INC (Iraqi National Congress) during a time when the Iraqi Liberation Act of 1998 put a high premium on trying to find a way to overthrow Saddam Hussein and to bring about regime change in Iraq," she told NBC, "and there were a number of organizations with which the United States had a relationship, including the INC. "

But Rice also said that President Bush "made very clear that the United States had no (opposition) force, so to speak, that it was backing. ..made very clear that Mr. Chalabi would have to make his way on the basis of his relationship with the Iraqi people — and that's still the case today."

Rice said she was "quite certain that the United States was absolutely vigilant in the way it should have been. ... We did have a relationship and it has been strained of late."

Fox News' Anna Stolley, Greg Kelly, Catherine Donaldson-Evans and The Associated Press contributed to this report.