NEW YORK (Reuters) - David Cameron will sit down with long-running U.S. television host David Letterman, CBS said Monday, marking the first time a sitting British prime minister will visit Letterman's "Late Show."

The September 29 broadcast will take place as Cameron visits New York for the UN General Assembly, CBS said in a statement. It did not say what Cameron would discuss. Former British Prime Minister Tony Blair appeared on the show twice, in 2009 and 2010, after he had left office.

Cameron is the latest top politician to appear on a TV chat shows offering lighter programming. Last week it was announced President Barack Obama and first lady Michelle Obama would make their first joint appearance on U.S. daytime talk show "The View" on September 25.

And Ann Romney, the wife of Republican presidential challenger Mitt Romney, will chat with a Letterman rival, late night host Jay Leno, also on September 25.

(Reporting By Christine Kearney, editing by Steve Orlofsky)