Brian Williams, who took himself off the air amid a deepening controversy about remarks he made related to his time in Iraq, reportedly has canceled a scheduled appearance on "Late Night with David Letterman" later this week. Sources told Politico and CNN Williams has decided against the Thursday night appearance.

Williams Saturday said he would take a "hiatus" from his gig as the anchor for "NBC Nightly News" after questions arose about his claims he was in a helicopter that took fire from rocket-propelled grenades and AK-47s when he was reporting from Iraq during the 2003 invasion.

Williams gave a vivid account to Letterman in 2013 and repeated it at a New York Rangers hockey game last month. Stars & Stripes reported last week Williams' claim his helicopter was forced down by RPG fire was false. The report said Williams' helicopter was nowhere near three other choppers that did take fire and made emergency landings. Williams arrived in the area about an hour later and landed because of an impending sandstorm, the report said.

Williams apologized for his statements, saying, “I don’t know what screwed up in my mind that caused me to conflate one aircraft with another.”

Williams was expected to be off the air for at least a week with weekend anchor Lester Holt filling in on "NBC Nightly News." Politico quoted NBC sources as saying the network is trying to buy time to see if the coverage will cool off but does not plan to suspend Williams.

CNN quoted a CBS source as saying a decision was made against the appearance on Letterman late Sunday afternoon.

Williams has appeared on Letterman's show 21 times, on NBC's "Late Night with Jimmy Fallon" 18 times and NBC's "The Tonight Show with Jay Leno" 13 times, IMBD reports. He also has appeared on "The Daily Show" with Jon Stewart 16 times and hosted "Saturday Night Live" once.

He currently has no other television appearances scheduled, CNN said.

There also are questions about Williams' Hurricane Katrina coverage. He has said twice he saw bodies floating after the storm that virtually destroyed New Orleans.

“When you look out of your hotel-room window in the French Quarter and watch a man float by face down, when you see bodies that you last saw in Banda Aceh, Indonesia, and swore to yourself that you would never see in your country,” he said in an interview with Michael Eisner, former CEO of the Walt Disney Co.

According to multiple media outlets, the primary problem with Williams’ statement is that he stayed at New Orleans’ Ritz-Carlton hotel during his time covering Hurricane Katrina. If Williams really looked out his hotel-room window, he likely would have seen water barely deep enough to cover the sidewalk, the News Orleans Advocate reported.