Taylor Branch and Haley Sweetland Edwards collaborated on this article. Branch is a Pulitzer Prize-winning author who first wrote for the Washington Monthly in 1969. His new book, "The King Years: Historic Moments in the Civil Rights Movement," is being published in January 2013. Haley Sweetland Edwards is an editor of the Washington Monthly.

In October 1961, Martin Luther King Jr. and President John F. Kennedy took an after-lunch stroll through the elegant hallways of the White House residence. Their meeting that day was not official: it was not in the White House’s appointment book, and King had not been formally invited to discuss any sort of business. It was instead a guarded and rather stilted introduction for leaders of professed goodwill, in a political climate that remained extremely sensitive about race.

When the men passed the Lincoln Bedroom on their tour, King noticed the Emancipation Proclamation framed on the wall, and took the opportunity to raise, ever so delicately, the pressing issue of civil rights. King suggested something radical: a second Emancipation Proclamation, a proposal that would become the centerpiece of King’s lobbying campaign for the next year.

Taylor Branch, the Pulitzer Prize-winning civil rights scholar and biographer of King, recently sat down with Washington Monthly editor Haley Sweetland Edwards and explained this idea, what happened next, and how Kennedy’s choice on the matter altered King’s thinking and the course of the civil rights movement.

How did the off-the-record meeting between King and Kennedy come about that October evening?...